4E had it right with using XP values and designing for an encounter, not a challenge rating. You cannot sum up the myriad of variables in any given encounter in a single number.
To be fair, 4e did assign monsters a level, it just didn't call it CR. But, combined with secondary role, it served a similar purpose. Level told you what monsters were appropriate for the party (from level -1 or 2 to level +4 or 5) to face, secondary-role told you in what numbers (4:1 to 6:1 for minions, 1:1 for standards, 1:2 for elites, and 1:5 for solos).
CR looks like level, but works a bit more like secondary-role, but is ultimately pretty murky by comparison. In the case of 3e vs 5e, the for every 2 CR lower, double the number appearing, guide may not have worked quite (nearly? at all?) as well as the 5e multiplier, but at least it was easy to remember.
Well, upon thinking about stories, myths, etc, There are 'lots' of stories about single 'boss monster' fights in the end, as they mentioned. I guess what I was thinking about was D&D and AD&D 1e/2e adventure modules....But that's all I can think of at the moment. Maybe there's more. I'm not including ones where the 'boss monster' is very likely to summon or otherwise 'have minions available'. I guess I'll have to concede there there are more adventures with "boss monsters" in them than I had originally though.
Or just "Number Appearing: 1." Any solitary monster is either solo-worthy, or not much worthy of being a monster, at all (and there were certainly some of both in classic D&D).
So there is still no real "solo" monster category in 5e, from what I can see.
Legendary seems pretty close. But, in theory, any but the very weakest lone monster fit the exp budget & difficulty encounter guidelines for parties of some level. In 5e, all monsters are meant to 'solo,' 'elite,' 'standard,' and 'minion,' to parties of a given relative level. That was one of the promises of Bounded Accuracy.