I think the reason why gen 1's EV system wouldn't work is because the whole idea of the current one is that you have to "sacrifice" something when making the Pokémon you want. Want a fast, deadly sweeper? You can maximize its Speed and appropriate attacking stat... but that leaves its HP and defenses low to act as a balance. Want a bulky wall? You'll have to train in the defensive areas, but it will leave your attacking capabilities lower.
So if all sweepers could be bulky, and all walls could be offensive, that just makes things... overpowered, for lack of a better word. The drawback of being able to max out only two stats is more of a balancing measure, and because you can only pick two stats it offers more diversity in terms of what you choose to create. For instance, in my happy Swampert family I mentioned above, if given the choice, I would absolutely give all of them all maxed-out stats regardless of what they were meant to do (it's kinda scary to think about a Mega Swampert that has maximum HP, Attack, Defense, Sp.Defense, and Speed...)--so then you have the same issue with IVs, where everyone will have the same EVs because why wouldn't you max out everything if given the chance?
Then the theoretical argument would be that EVs should be removed because everyone is using the same EV spread... when in reality our current EV system allows for creative freedom and should stay. But the reason why it allows for creative freedom is because it's limiting.
You even get cases where EV spreads can be very individual, too. Say you're certain you want your Pokémon to have max Sp. Attack, and be as bulky as possible. Well, that would be as simple as maxing out Sp. Attack and HP. But what you wanted it to be just a teensy bit faster to outspeed other similar Pokémon? That extra 4 EVs won't help you much. So you're gonna have to make a choice. Do you sacrifice some bulk?
244 HP / 252 SpA / 12 Spe
Or do you sacrifice some power?
252 HP / 244 SpA / 12 Spe
EV spreads can be as simple as 252 / 252 / 4, or as unique as 252 / 156 / 92 / 8. You can fine-tune your Pokémon to outspeed what you need it to, to survive what attacks it needs to survive, because of the nuances offered by EVs. But if you could max all stats? I can guarantee you, they'd all look like this no matter what the Pokémon: 252 / 252 / 252 / 252 / 252 / 252
In that case, I say going back to the gen 1 EV system isn't really even streamlining, and it would just make it so that EVs could be removed, in a similar vein to IVs.
Aside from that, though, it's very true that since Super Training was implemented, EV Training is more accessible as a whole. And horde battles are very, very great for EV training, too. I'm not sure how likely the removal of EVs are after those two things were incorporated into the games.