Rather than dropping unused pickups they should change it so that you can see what the pickups are going to be and there should be a time limit (say 30 seconds) between picking up another powerup once you have used your current pickup. For this scenario I think there should only be one pickup slot per car. The pickup slot would show a countdown timer once you've used your pickup. Because of the extremely fast speed which you are moving, they would probably need to add something to the UI which would indicate what the next pickups are. This would mean you need to think strategically about which ones you are going to pickup and which ones you'll pass by.
For example, you might not want a particular pickup but if you decide not to pick it up then the person behind you might pick it up and use it against you. Say I'm in the lead and the next pickups (side-by-side) are a speed boost and a lockon rocket; my car is badly damaged, so maybe I'll ignore these pickups thinking the next pickups might be health (which will fix my badly damaged vehicle - honestly I'm not sure why a health pickups haven't been implemented yet). But if I decide to pass by these pickups then my opponents might pick them up and use the lockon rocket to kill me or use the speedboost to get past me, but maybe I have enough of a lead so I take the risk. Maybe I don't have enough of a lead so I decide to pickup the boost in order to boost away from danger and get a bigger lead. Or maybe I pickup the lock on rocket so my opponents can't use it on me. If I pickup the lockon rocket so my opponents can;'t use it on me, I think have to decide do I use it/drop it and take a 30 second countdown until I can grab another pickup or do I hold onto it in case someone passes me.