I can give you some personal experience, based on my street 7 TwinCam and race TC in a Cortina.
The street engine used 2 Weber 40's with 70mm / 30 degree upturn stacks, and K&N pancake filters (~4"). The race 1600 used 45's, 50mm stacks, and Pipercross foam socks. Both were dry sump. The street engine carbs were relatively easy to setup, given all the Weber variables. Started every time, idled at 1000rpm (S2 cam), pulled cleanly everywere. It made about 30hp more than a stock Big Valve (130).
The race engine was setup on a dyno. It was basically a FB 1600 in a sedan. Cosworth and Brian Hart parts shared equal billing, and the head was ported by G.Villenue's Atlantic engine builder. 192hp @ 9000rpm - with or without socks.
On the track there was no definitive difference in lap times, using or not using socks.
There's no question they work in racing. As to, why no difference in dyno hp. My take is 192 is what that engine could make; the filters did not change the amount of available air required to do so. To me the simple leason from that is - if an engine makes less hp with filtered stacks, then unfiltered, then the filter(s) are c#ap. This is of course based on properly designed, and fitted stacks.
If you go to our website and go under photo gallery,go to Jim's H1 Kawasaki stacks, you'll see that stack design that we make is very similar if not identical to your top picture showing the functions of a velocity stack.
Sorry, have to disagree. I don't see a 1/4" radius at the entry for any of the stacks you offer. The stack draws air from all around the stack entrance. An abrupt edge will create turbulence, unless the inlet air flow has very slow velocity. The required radius has been cut in half for the H1 example.....
Sorry - I have to disagree. Honda (500/550/750), Keihin CR & FCR, Weber, and Dellorto, all use a bell mouth shaped as pictured. As an ultimate example of why it is not nessecary, look no further than the no holds bared CanAm injected big blocks. If a fully rolled lip would have made any extra power those cars would have had them.
High performance filters are generally rated for the hp they support. ITG make a Weber 45 filter that is rated at 200+hp. On my race engine that would have equated to x2 filters, and therefore support for 400+hp, on an engine making 192. Lots of breathing space there.
As I mentioned before, I plan on running the stock 77/78 stacks on my 550. Why? Because they fit properly (factory design); and from personal experience, and what I have read here, there will not be the pod flat spot tuning problems.