This has been on the table as a thing for a long time. Here's the long and short of the sitch.
First, we are planning on doing this eventually. Yes, they are allowed- multiclass profiles alone were rejected (even if I, to this day, disagree with the evaluation and think it was handled a wee bit unfairly). Class profiles have been discussed at length, particularly in the D&D work Discord between people like myself, Qawsed, Dragonstitch, and Tllmbrg.
Second, it would be based on levels, yeah. As far as I'm aware, most profiles would range from 9-B at base to High 6-A for main gameplay, potential Tier 2 keys for various epic level paths (things like ascending to godhood), and could reach up to potentially High 1-B when accounting for Mystara. The Psion page would have a 1-A key as well due to Topaz Crusader.
I don't know how we'd handle specific subclasses for 5e (or things like Prestige Classes from earlier editions). Likely they would have their own tabber and the sparse abilities provided by them would be listed there- I don't think ultimately they would change the profile much.
I need to make you understand something, though, since you seem to be implying something a bit iffy with the text- profiles wouldn't solely consider 5e. In general every edition must be considered unless something has been specifically retconned (so, say, "Elf" being a class). 4th Edition may require more scrutiny in this area since it is so wildly inconsistent on a lot of levels with other editions (MFTL+ and 9-A at 1st level as opposed to Subsonic and 9-B at 1st level, for example).