I think having to go down to pit speed limit would be a great introduction ,but you'd need the limiter to hold speed limit, have you tried holding 60kph/37mph. Possible but probably not for the length of pit lane.
As for F1CE style, like said before, drivers don't change tyres,so, that's a no from me, but possibilities to change compound on each corner(e.g.ovals) and fuel volume is a must.
I agree, getting down to pit road speed would be a cool challenge. Like a Nascar race at Daytona, you have to drop speed from 195M/H down to 55M/H by the yellow commitment line/cone at the end of pit road. Sounds easy, but you don't want to slow too soon, or too late to maximize your speed running up to and then make the best of the speed you have while on pit road.
Also, if we get a mile and a half track for Nascar, like Atlanta or Lowe's, you will be dropping off the banking of turn four, and slowing from 175-180M/H down to again 55, but the car will get loose while doing that if your braking too hard, it's just challenging. Cool though none the less.
Not to mention the pit exit at Daytona is down right scary on the road course, not much room for error. Just as bad on many tracks for F1 on pit entry, though they can use a limiter on pit road, getting down the twisty pit entrance without it, while going fast as possible will be tricky to say the least.
As for button mashing, I'm not sure, I'd like to hurry them up if I could, so it may be nice. I do hope we can do things like change our wing angle for cars that have them, adjust wedge or tire pressures for Nascar, or spring rubbers if PD is that gracious with the detail in Nascar. Pressing a sequence to spin the wedge wrench in the back window of the Nascar's would be cool, or move the analoge stick back and forth to press down some grille tape on the front of the car, or even a windsheild tear off for any car. Or if you don't do it right, the tape can fly off, or the tear off wont come off all the way and flap all over the windsheild until it rips off. There is lot's of stuff that it could be used for to make it pretty cool, I guess I'm undecided until I try a racing game with it. But I did like the adjustment setup for Nascar 2003 season

.