You certainly can remove the rockets, it just takes a lot of time and effort so isn't done for routine maintenance. Also, removing the rockets would probably be at least as dangerous as working with them there.

That's a shame. Nuclear weapons can be quickly/safely loaded and removed but the ejection seat rockets can't...

Ejection rockets seats don't need to be removed frequently. Nuclear weapons need to drop the instant someone hits the trigger. So why would you complicate the design of an ejection seat that needs to work under a wide variety of conditions?