You raise some interesting questions and certainly a lot of food for thought. I'll take a stab at one or two at least.
1.) Regarding the pointy tooth problem in traditional chronographs, I personally don't have the experience to know how much of an issue constant running is. Traditional chronographs with banged up teeth on the chrono wheel and/or the intermediate wheel are quite common, but I'm pretty sure more often than not the damage is done by watchmakers rather than just running/wear per se. I think there is some potential for damage from starting and stopping also, but the very fine tooth profile on soft metal gears is just asking for trouble on the service side. A watchmaker that is not quite careful (with the chrono wheel in particular) can do a lot of damage without even being aware of it.
I have serviced a reasonably large number of traditional (horizontal clutch) chronographs, but frankly other problems quite swamped any wear issues with the pointy teeth that might've caught my eye otherwise. I rather suspect (as you sort of hint) that much more is made of this issue as a point of discussion as it relates to vertical clutch chronographs than it really warrants from a practical standpoint.
2.) The amplitude drop is dependent on a host of factors and the vertical clutch is but one of them. The extent to which it is critical to running consistency is dependent on many other factors also (as you mentioned). There are vertical clutch chronographs that lose 30 or more degrees of amplitude with the chrono engaged on average due to their design but the Piguet 1185 generally loses very little amplitude or sometimes even picks up a little depending on the condition of the lubricants, etc.
There are some horizontal clutch chronographs that lose very little amplitude when the chronograph is engaged also, due to a friction coupled minutes counter. The Lemania chrono movement that serves as the base for the Ebel 137 and Breguet 582 is one of these. Depending on the particularities of the compound cannon pinion that drives the minutes counter, the movement can lose very little amplitude when engaged because it's just a tradeoff of one type of friction (the minutes counter clutch) for another (the friction in the chrono gears and tension spring for the chronograph wheel). The hour counter on most "traditional" chronographs is a similar friction clutch issue, but being driven directly by the barrel you don't really see any evidence of amplitude variation due to it being "on" or "off" (the hour counter specifically I mean).
Of course, the extent to which amplitude is critical to timekeeping depends on a number of variables relating to the escapement, hairspring and balance particularly. The Piguet 1185 is a movement that is served well by attention being paid to amplitude since it runs at a low beat rate with a smallish balance and a flat hairspring. Pairing it with a vertical clutch mechanism with little amplitude loss on activation is propitious (or at least prudent) I suppose.
It should be noted though that most vertical clutch chrongraphs suffer from floppy fourth wheel syndrome when NOT engaged. Basically, most designs put the vertical clutch right in the center of the movement and in the power train. When the chrono is disengaged, the fourth wheel (sometimes called the seconds wheel, which transfers power from the third wheel to the escape wheel) is free floating in the middle of the clutch mechanism. It's held in place by the geometry and set-up of the clutch mechanism as snugly as manufacturing tolerances will allow, but the nature of it floating on a post rather than running between pivots makes it inherently less stable. Basically, it kinda flops around a little bit, resulting in less than ideal consistency of power flow. This evens out quite a bit when the chronograph is engaged though, possibly another good reason to run the chrono all the time in such a design.
3.) I've got to agree with Jeff that this is a point where vertical clutch designs absolutely excel in comparison to transfer wheel mechanisms. Just ask anyone with a PanoGraph. Watching the chrono seconds hand jump backwards
when activated is pretty irritating to some folks. You're absoltuely right though that vertical clutches are not fool-proof in this regard though. If the scissor jaws for the clutch are damaged, misaligned, worn or otherwise out of whack, they can either release the clutch in an uneven fashion or at a funny angle that can cause a little jump when starting or stopping. It's not common in my experience, but it certainly can happen. It does mean something's wrong though.
4.) A fluttering chrono second hand is generally less of a problem with vertical clutch chronographs, but only necessarily so if the clutch is in the center of the movement (and carrying the chrono hand directly). Otherwise a tension spring is generally used on the chronograph wheel as it is on traditional chronographs. A fluttering second hand though is usually a sign that something is wrong (the tension spring being inadequately tightened most often), so it's not exactly a weak point of the design IMHO. I suppose the combined issue of amplitude drop and/or fluttering chrono second hand hand could be taken as a design weakness however since they are related phenomena.
Obviously Jeff is focusing on the design strengths of vertical clutch chronographs while completely ignoring some of their weaknesses, but as every engineer knows, there are no perfect solutions, only tradeoffs. In my experience, the biggest weaknesses in most vertical clutch designs are service related. It's easy for a watch enthusiast to think, "Well, that's the watchmaker's problem, what do I care?" but let me assure you that if you enjoy wearing a mechanical watch, the watchmaker's problems are your problems. Unless you enjoy sending your watch back and forth to the service center or watchmaker several times per overhaul that is.
For instance, the vertical clutch itself is a complicated, compound component that is generally considered to be unserviceable. It's also quite expensive (relative to other movement components). As such, any particularly conscientious service center is apt to change it at every service and pass along the cost to the customer. If you can't service the component to insure that the friction surfaces are in good condition and the lubrication is fresh and tidy, you can't know when it will fail, so you're asking for trouble if you simply set it aside and reinstall it (as is sometimes recommended).
Another problem with many vertical clutch designs is that the clutch and chronograph mechanism is so deeply integrated into the movement that you can't even run the base movement (to test its functionality) without assembling most if not all of the chronograph mechanism. This means that if a problem does arise after reassembly, it might be much more difficult to diagnose since you can't isolate the power train from the chronograph and vice versa. And woe be unto you (as a watchmaker I mean) if you discover a problem with the barrel at this point. You'll be re-cleaning the whole damn movement, chrono bits and all.
The latter problem is annoying (excessive integration reduced serviceability), but one that can be lived with IMHO. It encourages VERY thorough analysis and observation during disassembly and that's always a good practice for watchmakers to embrace. Occasionally some problem will still arise and piss you off, but those are the breaks with heavily-integrated, non-watchmaker-friendly designs.
The former problem however is more than annoying IMHO. It's really a matter of some philosophical debate whether or not a high end mechanical watch movement should have unserviceable components in it at all, but when they are big, expensive, absolutely critical parts, it starts to give me the willies. I can't help but envision a bleak future for the movement where scores of non-working or less desirable watches are canabalized for parts to keep the others running. Anyone see any good running Pierce chronos on the market lately? I didn't think so.