I was going to argue with this, since I remember it happening in gen II. Turns out, none of the Gen I fires got it until III at the earliest, and most as you said got it in IV. Gen II gave it to Houndoom, Entei, and Ho-Oh, but not Typhlosion or Magcargo. And III didn't give it to any fires except Ponyta/Rapidash for whatever reason. So Gen II was definitely making it a coverage move, giving it to most of the prominent fire-types, but they didn't update the Gen I movesets, and then III returned it to Grass+etc status, with a few serious oddities*. It's stuff like this that makes me question why GF has never sat down with a clear set of rules and started over on Movesets or anything like that. Because some things are just incoherent.
*Aggron, sure, it's reflective, but Mawile? Volbeat glows, but what's Surskit's excuse? And Gulpin and Flygon get it, which...what?
Gen III did actually update many previous generation mons to give them Solar Beam. A huge number of Normal-Type Pokémon — potentially all of them — and Beedrill also gained access to the Solar Beam TM in Gen III. From Aipom to Furret to Tauros to Lickitung, think of a Normal-Type Pokémon from the first 2 gens (besides Ditto) and it probably received Solar Beam in Gen III, though Chansey could learn it right from day 1!
Eh, I think it makes sense. Gen III was the introduction of doubles, where weather archetypes began being more viable as opposed to just having a weather setter and abuser in the same slot as had previously been the case in singles. Things were still pretty rudimentary at this point, so throwing Solar Beam on a bunch of Normal-Type Pokémon who have good TM coverage anyway was kind of sensible so that Sunny Day teams hypothetically weren’t just Fire- and Grass-Type Pokémon. That’s likely why they included it in the moveset of new Pokémon like Flygon, Aggron, and Mawile too. Probably just a gameplay thing to encourage players to try weather out while still being able to use their favourites. Hell, weather was a central theme of Hoenn from a gameplay perspective, what with the introduction of Groudon / Kyogre and Castform.
For what it’s worth, Thunder already had kind of insane coverage where almost everything could learn it (Primeape for instance!) but Gen III also added it to Furret and Stantler alongside Solar Beam, and continued giving it to odd cases like Banette, likely to help encourage people to use rain too.
Had Hurricane existed at the time, I’d certainly enjoy wondering how my Furret causes one of those too.
Edit (I really should learn how to multiquote properly on phone):
Solarbeam on Mr. Mime isn't strange to me. Given its emphasis on barriers (so much that it's in its japanese name), it might use a barrier to reflect sunlight, kind of like those rumored weaponized mirrors Archimedes had made.
Now, on Charizard NOT learning it... I find it weird, by default, that a Pokémon can learn Solar Beam but not Sunny Day.
By checking through a /ds command on Showdown, these are all the Pokémon that have that weird trait as of Gen VIII:
Abomasnow,
Alcremie,
Celesteela,
Coalossal,
Crustle,
Cryogonal,
Dottler,
Dragapult,
Duraludon,
Dwebble,
Emolga,
Eternatus,
Genesect,
Gigalith,
Golurk,
Lapras,
Magearna,
Melmetal,
Necrozma,
Ninetales-Alola,
Orbeetle,
Sigilyph,
Snover,
Vikavolt,
Zamazenta.
Many of those cases scream as either "it should also learn Sunny Day" or "it shouldn't learn Solar Beam in the first place".
Most of these kind of make complete sense for one of three reasons. Prisms, reflectiveness, and snow.
Did you know that snow is amazing at intensifying the heat of the sun? Kind of poetic, considering the sun also kills snow. I don’t have a great understanding of physics, but I think it actually works by reflecting the solar rays so the snow projects the heat from the sun elsewhere at a higher temperature than the sun puts on the snow itself. This might also be the work of prisms, but I’m not sure so I’m putting them in separate categories. This explains Abomasnow, Lapras (though Lapras lost Solar Beam from Gen II onwards), and Ninetales-Alola.
The second is prisms which do the same. Again, not a science guy, but I do know that prisms do something to light and it makes it stronger. I got a C in GCSE Physics, probably because I wrote that in the exam. Nonetheless it makes particularly prismatic Pokémon good candidates for Solar Beam. This explains Cryogonal (who kinda fits in both categories, but better fits here), Orbeetle, Gigalith, and Necrozma.
Sigilyph gets it because the Nazca Lines it’s based off of were situated in the desert and believed to absorb energy from the sun, pretty simple there. Zamazenta legit probably gets it because it wears a huge reflective shield. Emolga and Vikavolt also receive Energy Ball, and given Solar Beam’s far wider distribution than Energy Ball, I’d be surprised if anything learns Energy Ball but not Solar Beam (though I’m not sure why they learn either tbh, maybe just to dunk on Ground-Type mons despite being Electric-Type since they have an immunity too). Melmetal, Duraludon, Celesteela, Genesect, and Magearna get it because they’re shiny, and Genesect in particular learns most “beam” moves given its large mechanic cannon on its back.
I’d say it leaves Golurk, Crustle, Coalossal, Alcremie and Dragapult with difficult justifications. Crustle live in very hot and sunny places, and as the rocks on their back are dark they will absorb the sun and heat up, so with Pokémon magic it actually seems fine that they could use that absorbed sunlight as a beam. Hermit crabs shelter under rocks and shells specifically so the sun doesn’t bake them, in fact, so there’s a biological link for sure. Similarly, though not quite the same, coal is heated in fire in order to extract its energy. A fire isn’t quite the same as sunlight, but it’s near enough for Pokémon to run with. A much more sci-fi Pokémon like Golurk also almost doesn’t require an explanation — it
can turn into a rocket jet for some reason, so hey maybe it’s solar powered lmao. Dragapult and Alcremie I really have nothing for, but it’s notable that this list is just Pokémon who also can’t learn Sunny Day. Sunny Day itself is one of the most widely distributed moves in all of Pokémon, so the distinction of learning Solar Beam but not Sunny Day doesn’t mean too much. I suppose the point of this part of the post is to show that actually, in more recent generations Solar Beam has been distributed with reasonable levels of rationale. Certainly liberally, but still with thought.