Since you brought it up, I just checked the distance the trigger travels on the P250 and a couple other P series SIGs. The distance on all of them was pretty much the same, and the P220 and P239 were actually longer.
I dont have a 2022, and have never shot one, so I cant say one way or the other there.
Nothing scientific here, just measured from the start of trigger movement to let off.
P250....1/2"-5/8"
P6........5/8"
P220....3/4"
P226R....1/2"-5/8"
P229R....1/2"-5/8"
P239......3/4"
While they may or may not be a physically different trigger, I dont know, but the only thing I can see different with the P250's trigger is the stroke is noticeably lighter and nicer when you compare the DA stroke of all of them side by side, other than that, everything else is pretty much the same. Of the rest, the P239 came in second, and all the others, about even. Regardless, they all are easy to shoot well with.
Seems like all of this is just personal preference and maybe different thoughts on technique more than anything else. If any of the above pistols, or any other make for that matter, were handed to you as your issue weapon and you had to shoot it "as is" with no modifications, you'd either learn to shoot it well, or you wouldnt. If you couldnt, barring a bad gun, its still basically on you, and not the guns fault.