This becomes tricky, in the example used above, if an ability lets a character push another creature away, but then forces that character to deal with all kinds of annoying things like creature size. Suddenly, the pushing character is de-protagonized in a big way. Especially since traditionally, magic abilities have been allowed to do an end-run around the physics that the game has insisted on applying to martial characters doing the same kinds of things.
For your specific example, the easiest solution is not to rely on the rules to dictate what you can and cannot affect. This works for "tripping oozes" and "sneak attacking undead" the like, too, BTW. The effects that generate a "push" don't specify anywhere what types of creature they can and cannot effect, and the DM is given explicit permission and encouragement to make that decision for themselves. So in Game A, you can't push a giant, but in Game B maybe you can, and in Game C you can if you "describe it well enough." It is up to the judgement of the judge to determine if a given ability works, and the judge can always say "no." All the rules say is "This damages the enemy and pushes them."
One onion layer that might have some benefits (especially for newbies and casual players) is to have a generalized default that is easy to override. IE: Generally, you can't push a creature bigger than Large. Maybe in Game D you can, because they ignore that rule, because it's more fun for them that way. That has the benefit of easy judgment calls for newbies, but is also flexible without wrecking anything for folks who want other stuff.
To achieve this, we're going to have to tolerate that each table is going to be different, and that at the table where the DM doesn't let it work against giants and the adventure is all about giants, the ability won't be very useful, and that's fine. You shouldn't pick that ability in that DM's game. Pick something else. Player are not entitled to have their abilities work the same at every DM's table worldwide (but a given DM may very well grant players that).
I will note that this has not always been allowed. Sure, you could do this in chainmail or AD&D, or 3.x, but it had not been spelled out until 4e AFAIK. At least in AD&D, the prevailing mentality was "if it ain't on the page, it ain't on the stage" unless you got special permission from the DM, or you went ahead and researched a new version of a spell that reflected the changes you wanted to make.
I can't find the blurb right now, but I think it was in 2e, where specifically, the idea of magic missiles as screaming skulls came from. I think it was 2e because I remember the advice being kind of long-winded and unfocused, generally talking about how this is fine as long as there's no advantage to be gained. And there were examples of this as early as OD&D, where every monster was rather explicitly just a skin on some table stats, and the game talked about adding whatever the hell you wanted, as long as you gave it some numbers from that table. Re-fluffing wasn't invented in 2008.
I pointed out that 4e embraced this more fully than most other editions, but also that there was a cost for this: the wall that was built between gameplay and story was an intolerable thing for a big chunk of the player base. I'd prefer it to be more of a semi-permeable membrane at the level of the game rules, so that I can let them be basically the same thing, and a fan of 4e's iron-clad division could make them not overlap at all and we could all be playing the same thing.
This just underscores how brilliantly they will have to pull off the marriage of mechanics and fluff while leaving enough space to alter things as I am used to being able to do. As you say, the math is going to have to "work," but in my book that means it can't be working against the players' agency (as in the ToI vs a giant example), or I don't buy in, even as a DM.
I think the rules can be silent on pushing a giant centipede, because the DM can make the decision that is right for her table about that, and it can be different at different tables. It doesn't need to be a rule. It can be something decided in the moment. Alternately, the rules can have a default mode that is easy to override, without tremendously affecting balance or spiraling into complex rules interactions. Either way, you don't need to quantify exceptions in the rules text, you just need to give DMs permission and guidance about making their own exceptions.
That may mean that people whose fun relies on always being able to use their given abilities won't play under certain DM's, but that's fine. They can all still be playing D&D5e, because it's a big-tent kind of game, that abides the presence of people who are too strong about their magical elf preferences to have fun making funny voices and rolling dice together.