Once every few rounds. Big deal.
It's likely to be about every other round or so, in my experience, assuming a competent party that focuses fire. But I do agree that it's a useful addition. Using the bonus action for that in round 1 means you fall behind flurry-of-blows damage for that round, which is a little rough because the first round is the most important. Relative to a non-flurry round, you're about even --- 2d6 at the cost of 1d6+4, say. But if you flurry the next round, you gain 4d6 * (to-hit) damage --- maybe 9-10 or so on average. So you've increased your damage-per-round in the first two rounds by 4.5-5 or so. It's nice, for sure! Of course, you need to maintain concentration.
Actual baseline damage is about 2d8+8 per round, corrected for d20 swing, which the monk does at-will just like anyone else. The rogue does more on a hit because a miss hurts their output more, and everyone else (Including the monk) spends something to go past that. Maybe not the fighter, but they don’t get the third attack action attack until 11.
I'm not sure 2d8+8 is a really relevant baseline for anybody. First of all that assumes a one-handed weapon, so martial characters either have dueling style, or reckless attack, or sneak attack... Dueling style becomes 2d8+12... reckless attack increases damage output by about 50%. And then we get into abilities that use resources but are close to being "at will", like Hex and Hunter's Mark --- they're a 1st level slot for an hour of use. By tier 2 that's pretty indistinguishable from an at-will ability. And then you get into subclass abilities, and feats...
The reason Treantmonk uses EB+AB+Hex as a baseline is that it's an extremely simple tactic that involves a relatively no-brainer investment (take agonizing blast), is essentially "at-will", and is on a class that has lots of other features that they can use alongside that baseline. It's a low bar for damage for a martial class, because they're not bringing the other features that a warlock brings, so they'd better be better at fighting than the warlock if we're going to consider them to be carrying their weight.
The problem with monks isn't that they have to spend resources, it's that the return on those resources is really low, and they don't have enough of them --- even assuming a standard number of short rests! --- to go toe-to-toe with anybody else in terms of their bottom line contribution.
Unless it’s a battle where there are only creatures that will go down in 1 round (a boring, unchallenging, fight) then there are good uses of it.
A battle with creatures that go down in one round is just fine if that's happening with the group focusing fire, and if there are enough creatures that the whole
fight doesn't end in one round. If a typical combat is 4 rounds, say, then a combat with 4 enemies means that, on average, one of them is going down per round. With more than 4 enemies, on average more than one is going down per round. Unless the party is splitting up their efforts causing nobody to go down for the first three rounds and then all of the enemies to go down at once in the last round (which is just bad tactics), interesting fights (which means fights where there are at least as many enemies as PCs so that the party doesn't just curbstomp with their action economy advantage) you're typically going to have enemies going down every round.
That rogue is in serious trouble at my table, if that’s their strategy. They’re absolutely gonna need Uncanny Dodge.
The scenario we were discussing was one where the rogue takes their turn before the melee characters have closed into melee --- because otherwise they have sneak attack and don't need to ready. It's not a matter of readying an action every round; it's a first round tactic that allows the rogue (absent places to hide, or having a familiar in range, etc.) to get sneak attack off that round.
Both of you, and some other folks, seem to value ranged combat much too highly, as well. Do your DMs not include spellcasters, archers, flyers, and slippery skirmishers, in your battles? I’d consider any fight where the ranged characters are safe to be either an intentionally easy fight, or a fight that I failed to design well.
Who said anything about ranged characters being "safe"? They're saf_er_, because on balance monsters are stronger in melee, but I don't remember saying anything about ranged characters having no need for defense.
