I disagree with you on Specialist Priests. If you just look at the name, then yeah, but if you looked at what they can do and how they are designed, Cleric Domains don't fill the gap.
Sure. Some 'obsolete' classes could as easily be seen as still-needed classes, because the thing that obsoleted them doesn't actually let you play a descent facsimile of them.
It's also worth noting that even though there are some classes (concepts, really) that you can't do (or can just barely fake, if you squint really hard), there are others that you can do several different ways.
For instance, the classic elven Fighter/Magic-User (or just 'Elf' in /old/ old-school basic D&D). 5e PH, all options turned off, you could play a High Elf Eldritch Knight and you were doing the concept. Not very well, since you weren't casting until 3rd, and never got higher level spells, but doing it, however badly. Similarly, even with all options still turned off, you could play an Elf Wizard with the Soldier background, pick an additional weapon proficiency in addition to your elfy ones, and you're at least giving a /nod/ to the concept of also being a Fighter - on the other extreme, you could play a fighter with the Sage background and give a tiny nod to having studied magic.
Sot it's covered, right, you don't need anything else?
Wrong.
Turn on those optional rules and you can go right ahead and MC your Elf Fighter/Magic-user - OK, Fighter/Wizard - technically starting at 2nd level, but it's a lot closer to the concept. Or, if you wanted to go the Background 'nod,' you could double-down on it with a Feat to get a bit of spellcasting or some extra martial ability.
Sot it's covered, right, you don't need anything else?
Wrong.
Because, apparently, that wasn't good enough, or they wouldn't have put the elf-specific Bladesinger Wizard sub-class in SCAG, would they?
So, even if a class you like (like, say 3.x Sorcerer) gets listed in this thread as 'Obsolete,' that no reason to accept that you'll never be able to do something like it in 5e. And, yes, that's in spite of 5e /having/ an actual Sorcerer, with sub-classes of it's own. It just doesn't "do" the 3.x Sorcerer, conceptually (mechanically, the /wizard/ more than does the 3.x sorcerer, mechanics and artifacts of edition-differences are not the stumbling point, modeling the full range of concepts is), it'd have to have dozens if not hundreds of sub-classes the way it's designed to cover the same range of possible characters you could do with the Sorcerer in 3.x.
Because 5e is /wide open/ to doing the same concept in a number of different ways. And wide open to 3pp (OGL) and talented amateur (DMsG) contributions, too.