So the one thing linking all of them together is being a 3 stage line that ends in 600 BST. It's very specific at this point, like how starters are three stage GFW lines
It's like, Hydreigon is the gen 5 bloomer, not Haxorus or Volcarona, you know what I mean? Feels baked into their gameplay & design ethos.
Thinking about it, "Late Bloomer" is probably the best term for them as it goes with the concept that these Pokemon all seemingly followed:
Basic Stage: Now the initial thought is that the Basic Stage is "weak", some dex entries even saying so and some even having limited movesets. However if you just looked at their stats outside all other factors there all 300 BST, which is only a few points shy of Starters and above most other Basic Stage Pokemon that can evolve. Now some do "over-specialize" putting a ton of points into one stat leaving the others balancing out what's left which may leave a "weak" appearance in a way. However, that's not why they're deemed weak. They're deemed weak via comparison because it takes them so long to evolve. Most 2-stage and even some 3-stage Pokemon will be fully evolved or close to evolving by the time these guys evolve to their Mid Stage. By the time your team is around maybe Level 20 or so there are likely dozens of stronger options at that point than babying along the Late Bloomer who are less and less abling to take hits or dish out the damage.
Mid Stage: And even when they do evolve they're probably STILL behind a dozen other Pokemon available at that point! When they evolve they only get +100 or so points and those points are used not to push up the one or two stats that was high but to mostly balance out the other stats! You're lucky if one of their base stat is over 100, but if it is that just means all the other stats are going to be lower than average. But, isolating them from other Pokemon, now most if not all the Late Bloomers are able to hold their own in battle, able to fight back (the ones who had limited moves now get a bigger moveset) and take some hits. And while they may not excel in any stat that does mean they most often then not aren't lacking in a stat, a jack-of-all-trades but master-of-none deal. If the Basic Stage was that stubborn seed that wouldn't grow, the Mid Stage is that bud that finally broke to the surface and is very slowly opening up.
Final Stage: And finally one day you walk outside to the astonishing site of a beautiful flower that demands the attention of anyone who catches a glimpse of it! Upon evolving they get a major BST boost up to 600, a lot of those points put into one stat and the others graciously spread into the other stats that the Pokemon cares about. They're now learning powerful moves after powerful moves and the dex description sings their praises.
So, yeah, 3-stage and BST 600 is probably something that can't change about them because it's the structure the concept the Late Bloomer is built upon. Even the Starters I would say has a greater chance of breaking away from the 3-stage to maybe do a 2-stage or a gimmicky mono-stage for a gen. Not saying there isn't a way to do it, of course, with all the mechanics Pokemon has introduced over the years I could easily think of a couple things that could be done to replicate the Later Bloomer structure with a 2-stage or mono Pokemon (form changes, Ability that activates at a certain Level like Wishiwashi does, effect of a Signature Move, using the "super mechanic" of that gen, etc.). Heck, I'd actually be more willing to bet that if they ever introduced a 4-stage or even 5-stage Pokemon it probably would be for the Late Bloomer just so they could either make the Basic Stage weaker or gradually increase the middle stage's BST, lol.
I wouldn't be surprisd if gen 9 had a legend that could explicitly breed, which is otherwise a gimmick kept to Mythics ( Manaphy & Phione )
I'm betting one day they're going to have the Starters being the "children" of the Legendaries, revealing that certain members of the Starter species has the capability of transforming into the Legendary and the Legendary are able to breed more of the Starter species.