As I discussed before, as long as Eviolite remains in effect, cross-generational evolutions might be a specter of the past. However, with the recent expansion of Pokémon game universe into a multiverse in OR/AS, this might no longer be strict rule. Considering that, I will consider the two alternatives, one where side evolutions remain dominant and another where side evolutions remain with their current status quo.
Now, let's discuss why Side Evolutions are created in the first place. Unlike Baby Pokémon, Side Evolutions do not serve a direct in-game purpose, and their effect in marketing is minimal for the most part. The general reason why they are created is to give a different stat spread to existing Pokémon, for example, make Slowbro Sp. Defensive instead of regular Defensive:
However, more commonly the side evolutions are created to create gender exclusive variants of existing Pokémon, such as Froslass to Glalie:
There is also the third factor, Eeveelutions, which exist to have Eeveelutions of all types.
The fourth factor, which is to create grant other typings to existing families has been only significant for Froslass, Politoed, Eeveelutions and Bellossom, whereas others didn't gain anything from the alternative types. Though one can count Wurmple's Poison Sting into the mix.
So, what is the big issue then?
Well, here's the thing, side evolutions only work as branches out of the base Pokémon. They don't work as improvements to existing Pokémon, as they are designed to be equal in power to their counterpart, but since they are still different than their countepart, they are often given options exclusive to themselves. In fact, let's discuss them;
1.Forced seperation of side evolutions:
Virtually speaking, none of the moves that are not learned by Tyrogue is unavailable for all three Hitmons. You want to give Hitmonlee elemental Punches? Sorry, it is Hitmonchan's gimmick.
You want to give Agility to Hitmonlee? Sorry, it is Hitmonchan and Hitmontop's gimmick. You must use Unburden instead.
Some of these are logical, of course, but for the most part they aren't.
2.Limited convergence of side evolutions:
As we discussed before, the side evolutions are designed to be different with each other. So what happens when they are designed to converge with each other with their Base Pokémon?
Let's check Eevee:
Stored Power and Synchronoise for Espeon.
Fake Tears and Bite for Umbreon.
Charm and Baby-Doll Eyes for Sylveon.
These moves obtained for their respective evolutions can also be used for other evolutions, which is fantastic. But it is incredibly limited. Ideally, all of the Eeveelutions should give Eevee two to three moves to expand each Eeveelutions moveset. Otherwise, due to first rule, each Eeveelutions ends up incredibly anemic to be different.
3.One of the evolutions will be superior to others:
This is a bit related to power creep. As side evolutions are commonly created for each generation separately, the most recent one generally becomes the more relevant one because it is created with the status of that specific generation in mind.
However, this is inevitable as long as each side evolution have their ultimate potential squandered to be different than the rest.
So, why are they still relevant then? Well;
1. They reinvent existing Pokémon:
As said before, many of the existing branched evolutions reinvent the base Pokémon either by giving it a more steorotypically feminine/masculine evolution, or giving it a different play style. This grants extra value to the base Pokémon, and grants more options for base Pokémon to go through.
2. While convergence is low it still exists:
The two stages often bring something to each other, even if that is limited.
So what would be the ideal way to handle them?:
1.Differentiate two final evolutions significantly in terms of play styles:
Meaningful differences in play styles, that is. While the difference between Gardevoir and Gallade is significant, the difference between Bellossom and Vileplume isn't. To achieve this, several tactics can be employed:
a.Different sets of abilities:
This is largely present with side evolutions, but it bears repeating.
b.Drastically different stat options:
Such as different defensive and offensive options, instead of having the same focus but slightly shifted on which of the two focused areas have more focus.
Bellossom and Vileplume don't work as well as other side evolutions because they both focused on Special stats, the difference comes from the special stat they choose to focus on. Which doesn't effect their playstyles.
This is probably the best and hardest way to handle things. Different types give each Pokémon a different purpose, and a wide selection of justifiable exclusive moves. These moves can also be brought back to the originals to expand upon their own moves, and thus expand the whole family of side evolutions.
2.Increase the convergence between side evolutions:
The most ideal outcome would be that all side evolutions would be able to use all the moves they can use, but such a thing is anatomically impossible. As such, the ideal outcome would be that most of the possible moves are given to each species, preferably to their bases, as most side evolutions already share several moves exclusive compared to their bases.
As side evolutions haven't been used for proper in-game purposes, no one can say anything about their performance in those areas. So far, the only major in-game difference is that side evolutions that evolve by items can evolve at any level, and Wormadam's cloak gimmick.
However, an interesting way to use side evolutions would be to create new early game fodder using the same base. For example, create a new regional rodent that still evovles from Rattata. This would reduce the redundancy of base Pokémon, without changing other mechanics... that should be changed regardless.