Your first statement [JandK: "Part of what I'm saying is that I don't believe the balance is quite so delicate by far."]...could use some proof, but I'll certainly concede that D&D isn't perfectly balanced.
I'm not sure what kind of proof would satisfy folks.
But I think we could start by trying to agree on what "broken" looks like. In my opinion, it's probably something like this:
1. Does the game completely lack challenge?
2. Is the game basically impossible?
If we can answer either of those with "yes," then the game is probably broken in terms of balance. Otherwise, as long as there's challenge, but things are still winnable, then we're more than likely safe. [...]
I don't agree that those questions are sufficient. They are more appropriate for figuring out whether a game is brokenness in its entirety, not whether certain mechanic(s) are balanced compared to others. These are related but distinct questions. Importantly, when discussing balance of game mechanics in a TB tactical combat game, I'd include the very important questions:
3. Does a single (or small number of) abilities dominate such that they are near-universally used, such that many other abilities are NOT used?
4. Does a mechanic lead to less tactical options/thinking?
E.g., BG3 High Ground & Backstab Advantage led to practically every fight looking the same: ranged characters would go to high ground, and melee characters would circle around enemies. No need for spells/abilities that grant Advantage, just move 10 feet. Your questions #1 and #2 still were answered with "no" answers in this situation --- the Gith fight was still difficult but it was doable --- but these mechanics were definitely unbalanced, overpowered, and led to reduced tactics in battle.
Unlimited reactions would lead to much more damage (and damage mitigation) being put out during reactions compared to currently, as essentially you're giving characters additional actions as long as they use them on reaction abilities. However, this damage is also completely dependent on enemy actions, making it more random. This at least answers "Yes" to #4 imo, and possibly #3 depending exactly on how powerful these multiple reactions are. E.g., Reaction Battlemaster Maneuvers become much better, as they can potentially activate 3-4 times during a round. Brace + Riposte + Riposte can deal massive damage to an enemy that approaches and attacks you, much more than a fighter can output on their turn.