As much as I enjoy 5e, one design issue sticks in my craw: combat is too static. Once initiative is rolled, everyone tends to move to a single position and stand there whacking enemies until someone dies.1 Granted, the DM can deliberately engineer an encounter to encourage moving around, e.g., by including hazardous terrain features, forced movement, area effects, etc. But if every encounter is so engineered, at some point it begins to feel contrived. ("Whaddya know, yet another combat against monsters with push abilities set amid pools of burning lava. Darn our luck!") Besides, that's a lot of extra thought and work for the DM to put in. I like to make a DM's life easier... especially if it's mine.
Accordingly, the DMG's optional Flanking rule (p. 251), which grants advantage to attackers on opposite sides of an enemy, has an intuitive appeal. It at least appears to incent creatures to move around in search of better tactical positioning. And it requires little or no planning; it's entirely situational.
Yet most of the commentary I've heard about the rule has been negative. The main criticism seems to be that Flanking trivilizes the gaining of advantage, because maneuvering around an enemy is too easy and comes with no trade-offs. Whereas in past editions of D&D, moving while adjacent to an enemy invited danger (namely opportunity attacks), there is no such danger in 5e. As a result, the Flanking rule as currently written seldom requires creatures to make meaningful tactical choices about whether moving around an enemy in order to flank is worthwhile. Because advantage is powerful and the downsides of moving are insignificant, the answer to "is moving worthwhile?" is nearly always "yes" -- and so most combatants end up having advantage from flanking most of the time. That, in turn, devalues other mechanics that would grant advantage (the barbarian's Reckless Attack, spells like guiding bolt and faerie fire, etc.).
Another criticism, as this question suggests, is that rather than encouraging dynamic combat with more movement, etc., Flanking still produces static combat -- just combat in "conga line" formations of alternating PCs and monsters, all flanking each other. The accepted answer to that question supposes the conga-line problem can be solved by modifying the Flanking rule such that a creature who is flanked cannot flank another creature. I'm not sure that's true, but in any event it doesn't really address the main criticism that flanking, and the movement required to achieve it, is too easy.
Instead, I'm considering a house rule modifying Flanking such that a creature can't flank an enemy if there is any other enemy within 5 feet of the creature. The idea would be to encourage combatants to risk stepping away from enemies -- and drawing opportunity attacks -- in order to flank. That would tend to make flanking harder to achieve in the typical chaotic scrum of combat where enemies are all about, and so other options for gaining advantage would remain relatively valuable. And not coincidentally, it would also tend to break up conga-line combat formations.
What are the balance implications of such a house rule? Is there some class or monster ability that would be totally overpowered or broken by it?
1 For what it's worth, I apparently am not the only person for whom static combat is a concern.