Yeah, just recently though about weapons - probably because of Flatout 4. Could also be in Wreckfest - would/should not have to be part of the career - either in a quick race menu or similar to FO4 which has a "flatout mode" in addition to career and quick race.
Lots of possible gamemodes...
- you have one rocket per lap.
- or you have a railgun with a certain amount of ammo
- limited amount of NOS gas (almost like nitro, but based on reality, and no powerups)
- or take inspiration from the object cannon in the tech demo. You could shoot with all kinds of stuff.
- maybe even defence mechanisms like oil spills or smoke bombs