Is a water pressure booster pump with an induction motor suitable for kitchen tap use?
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?