Water – Low water pressure for water filter cartridges

I don't see induction motors as being particularly slow to start, so the answer is yes, it should be suitable.

There is no reason from a plumbing point of view why the booster pump has to be under the sink. It can be anywhere on the supply line to the kitchen sink. This may allow you to put the pump where it's noise is less of a problem. Oh, wait: If you are boosting the mixed water, it would need to be near. And if you aren't, you are going to pump water in circles through the mixing valve.

I dont see why an induction motor would be any quieter either. Noise may be due to resonance between the pump and the plumbing. This can be markedly reduced if you can use rubber hoses for the linkage instead of metal pipe. Mounting the motor on a resiliant pad can help too.

In general a more massive motor tends to be quieter, better bearings tend to be quieter. Induction motors may have better bearings.

Can the pressure in the whole house use a boost? Would a house sized booster pump and a pressure tank for the entire house be appropriate?

This is more of a comment but too long...

I was a pool boy through college. I have also owned 3 pools. What you are doing has too many variables. You have temperature, environment, chlorine levels, quality of original water, amount of swimmers, pump size, plumbing size, pool depth, almost anything around the pool is a variable.

So as a kid I would clean pools, add chemicals and often people had me set up their timers. But I was a dumb kid and was told 12 hours minimum and 16 hours for bigger pools. Usually in 2 shifts a day and we tried to set up timer to hours they were not swimming.

Some customers though set up their own timers and the times were literally all over the place. I have seen oversized pumps on for 2 x 2 hour shifts and the pool never had an issue (pool was in the middle of a yard not close to house, trees, and wasn't swam in a ton). I have seen algae grow in a pool that was being pumped 12 hours a day.

I would think that for your size pool and pump your baseline is 2 x 4 hours. I would consider 3 x 2.5 hours too. From there you can work your way down or up as needed. The big thing is if you are playing with the filter times then you need to keep an eye on the pool. You have to figure that each hour a day might be $8-15 a month in electric costs. But at the same time will you have to spend a ton of money on chemicals to fight an algae problem and all the time that goes with that.