I believe the way manufactures are handling the need for a more powerful flush today beyond what is ‘normal’ is to go pressure assist, not a higher tank height. Though that may be going away as modern designs do work well without the extra hardware that once was needed to get a low volume flush to work.
But I’ve seen some that also have a self cleaning mode where some form of cleaner is added. This takes care of the above mentioned smearing issue that most low flow ones have (as opposed to the old ‘swirl’ ones)
I see pressure-assist toilets (with a separate sealed plastic tank inside the porcelain tank used to store up pressure from the water supply without needing a larger pipe like in typical commercial flush-valve fixtures) in light commercial/office applications. I haven’t come across one in residential though because they’re quite loud. They do seem to work pretty well.
The water will come down faster, yes, but as the velocity of a fluid increases, its pressure decreases (see Bernoulli). You can also see if you pour a stream of water from a pitcher onto the ground that as the speed of the falling fluid increases, the stream thins out. In your scenario the water would enter the bowl at a higher velocity, but at a lower rate of volume/time.
I have a new toilet with two operating modes. If you simply push the handle down and release it, only about 1/3 of the tank empties. If you need more than that, you have to hold the handle for ten seconds or so. Or just 5 if you need only some more but not the whole flush. The plumber who installed it didn’t explain that to me until after I had a real clog that was very hard to plunge away until I also used a big flush.
They used a siphon (rather than a valve) in the cistern. The characteristic mode of failure (and reason most got replaced), was that the ‘pump’ action which primed the siphon failed due to wear and corrosion. So you’d stand there repeatedly pulling on the chain, softer, harder, slower, faster, trying to get it to flush.
Let me re-describe that. The actual volume/time is set by the flow restriction, not the length of fall. You don’t actually get /less/ volume just because the cross-section gets thinner. And Bernoulli decreases the static pressure in proportion to the /increase/ in the dynamic pressure. And the static pressure with a high cistern is greater. So at the bottom, the bowl, the you get a high-pressure flow.