I'm not particularly comfortable with the precedent of miners forking in sidechains, on which users blindly trust those miners.
But full nodes secure the network, not miners.
Bitcoin nodes only SPV validate the drivechain. That's the security model. Full nodes may enforce the drivechain rules at the Bitcoin consensus level, but that can't stop miners from stealing drivechain funds. 51% of miners can always steal all drivechain funds, no matter what. The only thing Bitcoin nodes can do to stop them is a UASF after the fact that reverses the theft.
Mining on the base layer could be worth more because it supports all side-chains.
Drivechains, extension blocks, and similar mechanisms are block size increases by another name. They offload transaction throughput, bringing cheaper fee costs to users. Would the base layer actually be worth more to miners? That depends if overall combined throughput increases enough to account for the cheaper fees. We simply don't know, and it's dangerous to rely on that. This is the block size and fee market debate all over again.
If you had a choice between a block size increase (soft or hard fork) and a drivechain, which would you choose? Why?