You may certainly rewrite the phrase in different ways. For instance:
“the worst thing that” ⇨ “the worst thing of all that”
“the worst thing that” ⇨ “the worst of all things that”
“the worst thing that” ⇨ “of all things the worst thing that”.
But none of these implies that the bolded form on the left is a “short” form of that on the right.
“that” ≠ “of all that”
“that” ≠ “of all things that”
“the” ≠ “of all things the”.
Neither of all nor of all things is present-but-omitted in that or in the. Neither is present-but-omitted in any of the words. The idea of of all (things) is ‘present’, not literally but by inference, for if something is “worse”, it must be worse than something to which it is compared, and if something is “worst” it must be worst of all things to which it is compared.
If you like, you may say that the idea of of all (things) is ‘made present’ in the -st ending on most; and that will be quite a useful notion, since it embraces not merely worst but also best and loudest and funniest as well—any superlative adjective, whether expressed with -st or with most. But when you get to that point it becomes clear that even the idea of of all is not “omitted”; it is merely not-expressed-in-those-words.
When you put of all or of all things into the sentence, or perform any other such transformation, you are not restoring something missing; you’re pointing an arrow at something you think is important, or ornamenting the sentence to make it more musical.
But all that is merely what FumbleFingers told you in the very first comment. And that, as tchrist told you (much more efficiently), “is simply the relative.”