How to get a missing effect back?

That really doesn't sound good.  

My guess (and it is a guess) is that there was an issue during installing.  Other than trashing your preferences, the only thing I can think of is uninstalling and reinstalling.

Then with no existing project open, create a solid and apply Card Wipe.  If that fails, I think reinstall is the only option.  If that succeeds, trying applying the effect to a old video you've never had an issue with.  If that succeeds, maybe there's something wrong with the project.

I'm sorry, these are just error identifying ideas,  but like I say, this is an issue I've never heard of before.

If after you've done all these steps, I think you should raise a ticket with support.  They've helped me in the past and are really responsive.

Trying to think of other reasons for AE to crash.  In my experience, most crashes have been caused by a conflict with the GPU.  Maybe double-check all your drivers are up to date.  Check if the project settings are software-only and that in Preferences Hardware Accelerated decoding is turned off.