A piano action would certainly influence the type of music one would make and the sounds one would use on a synthesizer. It would result in more percussive type patches and playing. Whereas, the traditional organ-type keyboard most often found on synthesizers allows for legato-type playing, which is the connected style that synthesizer music most often uses. Just try to play legato on one of the Nord or Roland piano action keyboards that offer organ, acoustic and electric piano, clavinet, and synthesizer presets. It's very awkward, and you settle into favoring the piano-oriented sounds.
A few years ago, I had a Roland FP-80 Digital Piano. It had the usual assortment of preset sounds, including pipe and drawbar organs. Playing such sounds on a piano keyboard was just bizarre, and there was no way you could achieve a perfect legato. So, I think it's for good reason that the organ-type keyboard has become the norm on synthesizer.