A possible solution to tanks sitting in HQs

I support this idea, but likely nothing will happen with it.

Vehicle camping (in or outside of spawn) has been an issue in most Battlefields I can remember. So yes a mechanic that would force them to move out of spawn would be more than welcome. Whether it should be a timer that makes the vehicle up for grabs (like you propose), or a timer that works like the out of bounds timer, or disabling the weapons systems while in spawn, can be debated.

The latter solution will not solve the issue of people camping the helicopter spawn. This is just griefing, but it can be easily resolved by implementing the BF2042 spawn system where aerial vehicles would spawn mid-air.

Prior to BF6 I listed mechanics that I would like to see in BF6 and back then I listed that jets and helicopters should spawn at base and not mid-air. I have changed my mind however, now I would rather go back to the BF2042 spawn mechanic for air vehicles. First of all to get rid of the people who spoil the fun for others by blocking spawnpoints or blast the helicopter with a RPG at the start of a match. 
And secondly I liked the timer in BF2042 that increased for people who just used the same vehicle. It had a double benefit, it would prevent people who use (read waste) air vehicles as taxi to quickly get from one point to another on the map to rinse and repeat, and also it would prevent these vehicles from exclusively being used by the same person all match long and instead giving others a chance of using it.