I've seen microkernels mentioned a few times between these LPE posts and I'm curious about why. Would they be fundamentally more secure against forgetting to add bounds checking, or assuming user-provided input buffers should be writable without checking?

Yes, because as a userspace program if you forget to do bounds checking or read the wrong thing, the kernel kills the process. But if the buggy code is the kernel then there’s no protection. Microkernels aim to have as little code as required in kernel space.