Q:

What is the impact of banishment on CR?

Disclaimer: I know that monster balance is never exact and I don't expect it to be, I'm looking for rough guidelines like they are given in the DMG for many traits.

I like to flavor up my monsters with spells. One spell that seems particularly interesting is banishment.
Monsters with that spell appear in the MM, e.g. the Death Knight, Sphinxes, and Guardian Naga. It is not clear however what effect the spell had on their CR.
I came up with the following assumptions:

It seems that since banishment is 4th level, i.e. for level 7 players, it should not appear below level 7 encounters.

Further, the spell requires concentration, but it seems reasonable to assume that a boss monster (no banishment for random critters) can hold concentration for some time through good saves, defense from minions, and, potentially, legendary resistance.

The effect of a missing PC is relevant for offense and defense since the party's damage output is reduced and the remaining PCs get more damage (relatively).

a priori it does not seem that banishment will get much better or worse on higher levels, since both the concentration maintaining capacity and the effect of a missing person seem to scale with level.

Are these assumptions valid? And how can these (and other factors that I might have missed) translate into CR?

A:

Don't use banishment, for reasons other than CR
Calculating CR
There is nothing about the spell banishment that means it should be treated differently any other monster spellcasting. Therefore, there is two things to consider, Save DC and Effect. Save DC is determined by CR so simply look at the table for that.
To determine if the spells effect should impact CR we can look at the rule for innate spellcasting under "Creating a Monster Stat Block" "Step 13. Special Traits, Actions, and Reactions" in the DMG:

Innate Spellcasting and Spellcasting. The impact that the Innate Spellcasting and Spellcasting traits have on a monster's challenge rating depends on the spells that the monster can cast. Spells that deal more damage than the monster's normal attack routine and spells that increase the monster's AC or hit points need to be accounted for when determining the monster's final challenge rating. [...]

Banishment neither deals more damage than the monster's normal attack (it deals none) nor increases the monster's AC or hit points. So by RAW it has no impact on the CR of the monster.
Why you shouldn't use it
Getting banished sucks.
Banishment is a great tactic for the party to use. Separate the threats by sending the biggest away until you can prepare for them. Get a few rounds of healing in during a fight that's going badly. Straight up end encounters with extra-planar beings. These are all good, cool things for the party to do and therefore fun for the players.
What isn't fun, is losing your turns stuck on another plane while you watch your friends get killed. Banishment is one of those spells that take away a player's agency, there is nothing they can do about it short of casting plane shift and that's spending a 7th level spell to counter a 4th level one. Also not fun.
Giving banishment to a monster won't increase its CR, but it will decrease its FR (fun rating). Don't make monsters less fun to fight. Avoid spells that prevent players from participating.

A:

I don't think your assumptions really hold.

It seems that since that since banishment is 4th level, i.e. for level 7 players, it should not appear below level 7 encounters.

There's really no problem with adding Banishment to a CR 1 creature. It just removes one player from the fight for a bit, which isn't fun, but probably less harmful then standing around Paralyzed, which numerous CR 1 creatures can do.

Further, the spell requires concentration, but it seems reasonable to assume that a boss monster (no banishment for random critters) can hold concentration for some time through good saves, defense from minions, and, potentially, legendary resistance.

Honestly, the odds are not that high. Players are likely to wail heavily on an enemy spellcaster holding concentration and every point of damage triggers a roll. Don't expect the boss to hold concentration for more than 1 round, 2 if lucky. Also, wasting Legendary Resistance on concentration saves sounds like a waste.

The effect of a missing PC is relevant for offense and defense since the party's damage output is reduced and the remaining PCs get more damage (relatively).

Mostly for missing offense. Compared to all other option for temporarily shutting down a PC, this is the least harmful one. See above, most other options keep the PC around in a shut-down state, which makes them easier to damage. Yes the remaining PCs get a few more hits, but that's better than the locked down PC being smashed to death.

a priori it does not seem that banishment will get much better or worse on higher levels, since both the concentration maintaining capacity and the effect of a missing person seem to scale with level.

This is mostly fair; assuming the level of Banishment is the same. Higher level Banishment can target more creatures. It could get annoying when these fights happen on a different plane and for whatever reason the boss can concentrate for a minute and your friend is missing across the multiverse. Then again, the only reason a fight lasts that long is because the players retreated, in which case a paralyzed PC is also going to be in trouble.
So what does Banishment do in terms of CR?
To be honest, I'd say "nothing". Your monster spends an action that will remove one PC from the fight for about 1 round, maybe 2 if it's lucky. You lose out on a full round's worth of damage to gain a few extra HP in terms of damage saved.
I ran a game with a monster that could not only Banish people, it dealt pretty serious damage to them every round while they remained banished. It was also beefy, with like a +5 to concentration saves and superb resistance to magic.
It was CR 4 and part of an encounter for 5th level characters, and while scary (mostly because they had no idea what was going on initially) it ended up not killing anyone, even though it had some other minions hanging around.
Based on that, I'd say that simply adding a default Banishment to a monster might raise some eyebrows around the table, it's not going to end up making your monster too powerful.

