Using the stick to accelerate and brake seems insane to me in an age of triggers. What's next, asking to return to having steering on the same stick too? Remember Pit Stop on the C64? Great game, but your hands would be destroyed after one race holding up on a stick for a whole race.
It's backward thinking for a number of reasons.
1. You can't brake and accelerate at the same time. Case in point: Burnout Paradise 'burnouts' to start events.
2. Sort of related to point 1, precision cornering would be difficult, as you have to stop accelerating entirely in order to tap brake.
3. Degree of motion would be less on a stick, as the distance it travels is shorter.
4. Thumbs aren't as agile as pointer fingers leaving a lack of accuracy (movement in a third person action game for instance, it's difficult to find the sweet spot of slow walking and running on an analogue stick).
5. Your fingers are sitting there regardless if there's triggers or not. So you'd want to use them for something. What else would you use triggers for in a racing game?
6. You could accidentally brake instead of slow down, due to both movements attached to one input. For instance, accidentally hitting brake instead of just easing off the accelerator could spin you out in sim style racing games.
7. Where would you map the camera? In some views in some racing games, adjusting the camera up or down so you can see better when going up or down a hill is necessary.