Although the turbo does stall with no BOV, the pressure in the intercooler and pipework between the turbo and inlet drops away much more slowly than it does with a BOV.
So, when changing gear quickly the engine receives boost straight away rather than having to wait a split second for the boost to build up again. The turbo does need to spin up again but this loss is outweighted by the benefit of keeping pressure.

The car makes a lovely sound if you run with the BOV blanked off... throttle response is actually improved to... it will, however, subject the turbo to a new series of stresses.

Having a BOV on a turbo engine reduces throttle response, it allows boost that would be there to bleed away.

If you want to run without a BOV to get better response then a good idea is to use an uprated turbo with a 360 degree thrust bearing. (I have run normal 300 degree bearing turbos without BOV's for over 12 months on track days and road without a problem.)

There is another factor to throttle response. That is what presure is in the system between the turbo outlet and the throttle butterfly when you open the throttle. If you have a BOV in the system, when you come off throttle the boost presure is bled away. What this means is that when you re-open the throttle buterfly the turbo has to build the boost back up.