It occurred to me while reading the line "He was as happy as could be." that part of it is quite vague. As happy as he could be, or as anything could be? I'm not a linguist or anything, but I haven't been able to think of anything that follows a similar pattern, without following the pattern exactly (as in the title of the question).
Regardless of how well it is understood by others or how often it is used (unless this affects the answer), is a phrase like this bad grammar?
Well, there's no God-given list of pieces of grammar that are "bad" vs pieces of grammar that are "good"-- just people who invent arbitrary reasons for labelling things as such and then other people who decide to agree with those reasons.
So, you've invented your arbitrary reason for deciding it's "bad" grammar. You just need to decide to agree with yourself and you're done...
A similar pattern would be "He was as happy as is possible".
No he or anybody there either, but it is implied.
If you pair it with a superlative, e.g. "perfect as could be," it would be redundant, but other than that I don't see any problem with it.
Sometimes in English we have phrases that have been in use for so long, that some words have been dropped out. My guess is that the commonly used phrase "He was as happy as could be" is an ellipsis of something along the lines of
He was as happy as [he] could [ever have expected he could/might] be.
Possibly the words were eliminated because of the two 'could's, and/or also because the phrase was used so much that people developed a sense of what others meant. I would guess that there are quite a lot of other examples like this, if we dig around.
