You need to be a little more specific about what a soft pedal is. Also, the age / mileage of the car might be useful. I assume soft pedal means that you are getting more than what you think would be the normal amount of pedal travel? You did not mention loss of brake fluid so I assume that the system does not have a leak which could be a cause for loss of hydraulic pressure and a soft pedal.
Check the brake pedal play / pedal height as described in the service manual. Excessive push rod clearance clearance does not create a 'soft pedal'; but, will result in excess pedal travel before generating brake system pressure. If the pedal play / height measurement is correct do not adjust it. There is also a push rod clearance adjustment at the brake booster - master cylinder connection point. Normally this would not be an issue or change unless the MC or the booster had been removed for some reason.
If you apply continuous pressure to the brake pedal does it gradually sink to the floor? If so and the car is early production or high mileage a possible candidate is the master cylinder. The seals on the primary or the secondary piston in the MC may have failed which is allowing fluid to leak back into the MC resulting in increased pedal movement. Depending on which piston seal (primary / secondary) has failed the pedal will respond differently. The NSX does not appear to have a pressure differential switch that detects this failure mode. If the secondary seals fail this affects the rear brakes and you may not notice a huge change in brake performance. If the primary pistons fails that affects the front brakes and I expect that the loss in brake performance would be very noticeable. Depending on the nature of the seal failure the pedal may not sink completely to the floor, you just have excessive pedal travel.
How long have you had this soft pedal problem? Was the brake system ever flushed / bled by using the pedal pump method? If so, and a pedal block was not used to restrict the travel of the brake pedal the seals on the MC pistons may have been damaged when they were forced past their normal wear ridge. Once a vehicle has several thousand km on it you need to use a pedal block to restrict pedal movement or bleed using a pressure bleeder or a vacuum bleeder (the latter two are best).
With new fluid in the system the pedal is exactly the same as before, the mechanic suggested this could be because of the 'slower' bleed caliper rather than the master cylinder or servo as the other 3 calipers bleed at the same flow rate.
I am not sure how slow bleeding from the caliper would cause the problem unless there is already air trapped in the line to the caliper or the caliper itself. If the flow rate during bleeding is incredibly low this may result in failure to move the air bubbles so that they remain trapped. How was the brake bleeding done? Did they use a pressure bleeder? If so, the pressure in the system should have been enough to move any air bubbles.
If you suspect that the MC is the problem I would just replace with new. I believe that there may be rebuild kits available; but, if you re use the MC housing the it has to be honed to remove the wear ridge other wise the new seals will be destroyed on the wear ridge. If the housing is really worn it may be too far gone for honing. If you are paying to have this done it will likely be be cheaper to do outright replacement rather than pay somebody to disassemble, hone and rebuild.
