Zombies remain in the process table for a reason: There's still information there about how the program quit, which their parent is supposed to get via the wait() or other related calls. Once it does, they're deleted from the table.

init can't wait for processes that don't belong to it. If it did, that could cause problems with processes that were handling their children -- if init handles the dead process first for whatever reason, the proper parent will be stuck waiting for it.

So, only the owner of a process is allowed to wait() for it.

So a process that accumulates an endless amount of zombies is a serious problem. There may be limits in place preventing one user from running too many simultaneous processes, but often these limits haven't been specified for daemons. It's possible for the process table to be filled up, yes.

The proper way to deal with zombies is to fix the bug in the program that's allowing zombies to accumulate. The short-term solution is to kill their parent -- all the zombies will default back to init, which will clean them up.