Dear Jer,
Yes, the ball needs to "feed" down the one and only one fall-line thru the hole, which has some interesting consequences. The biggest one is that the golfer should NEVER allow his ball to cross over the fall-line high side. That speed is trying to "feed" down one of the thousands or millions of nearly parallel OTHER fall-lines thru locations near the cup on thwe far side of the desired fall-line. Also, the ball should not be baby-ed so that it ends up "feeding" down a fall-line short of the fall-line desired. So, sort of, the "perfect" touch has the ball feed onto the correct one and only fall-line right before it falls over the lip, on the 6-12 line.
Now, as to your second point about putting with a little extra speed: yes, every putt with instinctive touch inherently has a little extra speed in this sense: the speed of the ball crossing the lip is more than "zero plus a tiny bit" (zero plus "iota" in mathematics and physics), but not all that much. A golfer learns from adapting to the reality of ball-hole capture physics that 2-3 revolutions per second over the lip on a fairly level slant is usually just about the right balance between three factors or requirements for good touch: 1. get the ball over any junk all the way to the lip; 2. arrive at a speed that keeps the effective width of the hole nice and wide; and 3. don't arrive with more than necessary for (1) so as to avoid long comeback second putts in case the ball misses.
In the specific case of a downhill putt, versus a sidehill putt, there is only ONE sidehill putt (either from 3 or 9, precisely and only), whereas there are putts above the 3-9 axis that are somewhat downhill and putts very downhill, until you get to 12 where putts are completely and only downhill. As the back of the cup is more tilted downhill on these different trajectories, the optimal delivery speed gets a little slower as the putt's starting position goes higher from 3 or 9 towards 12.
AND, since the sidehill putt always starts off in a path that combines sideways with a fair degree of uphill too, and 12 has NO sideways component, then there must be some starting point between 3 or 9 and 12 where the starting line of the putt is completely and only sideways with NO uphill component at all. This one special starting position is determined by the golfer's delivery speed, the green tilt, and the green speed.
If EVERY putt crossed the lip of the hole with exactly 2 revolutions per second (or the same speed as you choose), regardless of the starting position of the ball for any and all possible positions either left of right of 6 all the way up to 12, then this sideways-only position is likely somewhere near 10 or 2 in most cases of green speed and tilt. As the green speed increases or the tilt increases, then this special position goes closer along the clockface edge towards 12.
Looking at the same phenomenon but starting with the height of the target location a certain distance up the fall line from the hole center towards 12, this special sideways-only position out on the clockface edge MUST be whatever is LEVEL with the height of the target, left or right.
A little trigonometry shows the following relationship between height of target up the fall line (i.e., "apothem") and starting position out at the edge of the clockface around the hole inside of which the surface can be characterized a "flat but tilted":
11 and 1 o'clock are 86.603% up from the center of the hole to the 12 on the edge of the clockface
10 and 2 o'clock are 50.000% up from the center of the hole to the 12 on the edge of the clockface
9 and 3 o'clock are 0.000% up from the center of the hole to the 12 on the edge of the clockface
Hence, if the edge of the clockface and the 12 is 1 meter / 39.37" from the center of the hole (beyond which the surface is no longer really "flat" but has other undulation if not tilt also), then 11 and 1 o'clock are 86.603 cm / 34.096" up the fall line from the center, and 10 and 2 o'clock are 50 cm / 19.685" up the fall line from the center.
For every 12" from center of hole up to the 12 on the edge of the clockface, there are 10.4" of rise up the 6-12 line from the hole center to get horizontally beside the 11 or 1 o'clock positions, and 6.0" of rise up the 6-12 line from the hole center to get horizontally beside the 10 or 2 o'clock positions.
These relationships are general and quite difficult to estimate or predict with precision in specific practice due to the interrelationship of tilt, surface speed and ball rolling speed. My sense is that the otherwise very precise intuition may not quite be up to this particular task at the desired level of precision and consistency. Some experimentation, though, can fill in the blanks with some specific sideways-only startline heights for given tilts, green speeds, and delivery speeds.
The point is it would be very interesting to know where this sideways-only starting position is located for certain typical tilts and green speeds for the "usual" instinctive touch. In my approach, once this location is known, and whenever the ball startline aims horizontally at this target, the golfer simply putts level horizontally sideways at the fall-line as if to sink a putt into a hole centered on the fall line level with the starting position of the ball. Then the ball enters the real hole with the "usual" delivery speed you use (e.g., 2 revolutions per second over the lip), feeding exactly onto the fall line right at the last before disappearing over the lip.
This sort of sideways-only putt occasionally shows up at Augusta National from about 11 or 1 on the clockface.
Any putt below this sideways-only starting point has some degree of uphill component in its start line, and any putt above this special point has some downhill componment in its start line. This clarifies breaking putts a bit!
Now, to your exact question: whether a ball that "feeds" onto the 6-12 fall line thru the center of the cup with more room for error is also "harder to do" than adding a little speed so the entry path is not quite on the 6-12 fall line as it crosses the lip but closer to the 3-9 line to some degree?
To my mind, the answer is "not really". While feeding onto the fall line takes a little less speed than the usual speed due to the back of the lip being a smidgen more tilted down away from the approach path of the ball than is the case with a slightly lowered path with a little extra speed, the difference in the back of the cup being lower in the first case than in the second is very minor, plus the speed that can safely be added to "take a little break out" (as Ken Venturi tirelessly and tediously repeated ad naseum on CBS for years!) is not really as great as people think, so there is really very little difference between the two speeds.
What confuses people, I think, is not distinguishing between "close" putts where the golfer can more safely hit the desired line when taking out a little break and more medium-length cases where adding some speed is not all that safe in light of the greater tendency to wander off the precise line from this middle distance. In the case of "close" putts, people think adding speed is easy (due to the easier ability to hit the line and get the ball to the hole before line error off angle really starts to tell). This is usually the case inside three feet, and maybe really only inside two feet.
Consequently, hitting the lowered line only seems easier in "close" putts. What people asppear to be comparing in making this judgment are "close" lowered-path putts with not-so-close "feeding" onto the fall line putts. But if the comparison is not apples and oranges, but apples and apples, then the answer to your question is a lot more solidly "not really." The speed of both putts CAN be the same in "close" putts, as speeding up the delivery to feed onto the fall line simply lowers the target spot on the fall line to "feed" the ball at initially, but since hitting the desired line without any error telling before the ball is into the cup is the same for the lowered path as it is for the "feed" path with the lowered target (speeding the ball in the lowered-path putt also lowers the target spot down the fall line.)
The best advice I can give is "stay smooth" in all cases so as not to "baby" a putt and not to "ram" the putt thru any break. That's the same whether "feeding" the ball onto the fall line or adding a bit of speed to take a less-breaking line.
Cheers!
Geoff Mangum
Putting Theorist and Coach