What can they do to stop you if your phone is capable of installing a recovery?

They can always fall back on statutory protections. They can also do OS detection and boot units that smell fishy.

How can they block custom ROM's? Let me count the ways!

-signed bootloader

-encrypted bootloader

-e-fuse

-not disclosing drivers

-legal threats for implementing proprietary drivers/ software

Not letting you install a recovery.