I'll try to answer your questions the best I can and hope other forum members will join in to help.
True that many discussion here on the forum are on vintage pieces but that's mainly because many of the forum regulars (including yours truly) are great vintage fans. This is certainly subjective but VC not only has probably the greatest diversity in terms of designs for their vintage models but also these pieces are the most beautiful available (for some examples check the photo gallery)
The modern pieces are extremely popular and if you read past posts you will see that there has been many discussions on current models.
VC's strategy is not based mainly on really expensive pieces but by essence their watches are expensive. An entry price Patrimony small seconds is approx euro 8000 which is in line with the other Swiss houses you mention. There may be no signature model like the Royal Oak or the Lange 1 (I prefer not to mention the Calatrava which in my opinion cannot be considered as a signature model since the name just refers to PP's round timepieces) but for some the lack of a signature piece is detrimental to VC while others state that it is a good thing since it gives more freedom to the brand and does not make it dependent on just one model (imagine what would happen to AP or JLC if the RO or the Reverso stopped being fashionable!!)
VC as of today makes about 15000 pieces a year which is way under what the other two great Swiss houses produce. I don't know about sales but if the CEO is still in place then the sale figures must not be too bad
I agree with you that there is much less noise about VC than AP or PP but I like to think of VC as a sort of old English gentleman's club where with a slight nod of a head you recognise a member. Something like you have to be in the know to appreciate one
VC certainly does not have the Patek mystique because to say it bluntly PP has been working on creating the image they have today over 20 years ago, they supported auction prices (to a point where unfortunately when you read the PP forum most questions are on investment value but not on the watches themselves, many of which by the way I like a lot), creating a museum and generally creating the impression of extreme rarity for certain pieces (for me this is unimaginable: but if you want to buy a complicated Patek you actually have to send a motivation letter to Mr. Stern asking him to sell you a watch!!)
Why do I like VC today? Well, one thing is that even though they are 250 years old they try to come out with new designs and models (even though they don't always get it right
) and not just copy past creations resizing them to today's tastes. I like owning a watch by a brand who has been around for a quarter of a millennium (on this note I admit I love their current add campaign, puts everything in perspective), I like the fact that they still use almost disappeard art forms such as enameling, engraving and skeletonising, I like the fact that they will be launching in the next months a custom make atelier where you can commission anything from a different dial for your Patrimony to a Grande Complication, I like the aura of the brand, I like its mystique and in a way I like the fact that it is less talked about than other brands... call it snobbery