Everything can "break the game" when you give the players enough freedom. So either you restrict the freedom of your players heavily, turning 5E even more into a board game than an RPG, or accept that there will be no perfect balance.
Even more, you can only "break" the game when you have a very specific vision of how the game should be played (most often tactical combat dungeon crawling) and allow no deviation from it (either because of preference or lack of rules).
As soon as you expand the scope of the game it is much more difficult to "break" as it consists of more than just one activity.
The only scenario that I can think of where a game absolutely cannot "break" is under the auspices of a playstyle that is underwritten by a (i) complete anarchy of direction/focus with respect to genre emulation and where there is the acceptance of (ii) an utter vacuum of mood, tone and pacing. The moment (i) or (ii) moves even slightly from anarchy and vacuum the game will absolutely "break" when elements are introduced that undermine any of those. So you actually have it 180 degrees backward. The number of playstyles that are excluded are pretty much all but that narrow playstyle that is premised upon (i) and (ii).
If I throw guys with laser guns or space clown aliens or Taco Bells or rocket skateboards into a "spaghetti western paced" based game or a "feudal setting game that presupposes limited archaic levels of tech" or a "No Country for Old Men mood" game...that game becomes inevitably "broken". If I have a game where I want horror and fear to be a strong undercurrent and the PCs are so powerful that the threat is rendered inert or the "horror mechanics" become irrelevant then the game becomes inevitably "broken". If I want exploration of an ancient, enchanted forest to be truly relevant...to be scary, wondrous and interesting...then there cannot be readily available resource schemes or tools that customarily bypass this aspect of the game such that it becomes standard operating procedure to fly over the forest or "ask a tree where the important thing is" and teleport/tree stride there. I could write a book on this of examples. Anything that isn't genre anarchy and an utter vacuum of mood, tone and pacing can be broken by elements that don't comport (or are in outright discord) with the implied setting/genre or player resource schemes that lead to unbounded power and thus lead to inevitable, absurd SoPs that allow PCs to fully bypass challenges by just not engaging with them. In homage to the week of its anniversary, throw a D&D wizard into "The Princess Bride" and everything that makes that film great ceases to exist. Every scene becomes "broken."
Contrary to your position, anarchy of direction, unbounded options/power narrow PC choices and they narrow the scope of potential gameplay accordingly as power play gimmicks become standard operating procedure. This is especially so in a game like D&D where nothing but absolute success is incentivized as failure is uniformly and ultimately punitive...where it narrows the scope of the game in the most complete way; TPK/campaign ending.
And what this has to do with "tactical combat dungeon crawling" I'm not really sure.
Like Greyice posts above, I hope every weird, overpowered oddity of D&D history (and new ones) are available to players for 5e. But there really needs to be DM advice for just what these components engender within play and what scope of play they crowd out...because in my experience there are an abundance of playstyles out there that are excluded by the "genre anarchy" and "mood, tone, pace vacuum".
