There is light contact patch reduction compared to larger diameter tyres. For the same width and optimized pressures, the contact patch is approximately inversely proportional to the tyre load rating. Stock 16s are 1201lbs. 205/50-15 are 1168lbs, 225/45-15 are 1201lbs. 16" autocross were 1168lb So, my contact patch is about the same. Except that the autocross tyres tend to be somewhat wider than street tyres, so may be able to run lower pressures.
Class rules limit wheel width and offset, so I can't take advantage of wheel poke to put enormous tyres on.
Tyre availability is a big factor. The choice in 16" is way smaller than in 15".
Lighter wheel/tyre weight will help a bit with acceleration, but not as much as some 'experts' will tell you. It also help keep the wheels on the ground. How much is again, a bit contentious, it depends a mainly on how good the dampers are. Lighter wheels do make a huge difference to ride. This course is relatively flat, some are quite bumpy. Lighter wheels also reduce gyroscopic effects, so I can yank on the wheel at speed and it will turn faster. Power steering obviously helps this factor disappear, but it does affect feel.
The smaller diameter does make a difference to effective gearing. These tyres are 3% smaller than the 16s I was autocrossing on, and 7% smaller than stock tyres. That is quite noticeable.
One last advantage, they are the only legal way to lower the car in street class. That means less weight transfer and less roll. Both of which help with both handling and ultimate lateral grip. Shorter springs will mess up stock geometry and cause more roll of the stock stiffness.
I don't know how much the different tyre model, reduced weight and smaller diameter are individually contributing, but the overall package feels just great.
Take all of this with a pinch of salt, I'm sure as hell not the fastest guy out there. I'm just quicker than I used to be.