Hear me out on this. I think one of the big reasons people are so disgruntled about the EX Raid system is that Niantic has fostered the idea that everybody is entitled to every legendary pokemon (and multiple copies of them). If legendary raids were all EX Raids that happened more frequently, e.g. every day or two in a given area, but with a random legendary pokemon, then people wouldn't be so upset about having some legendaries, but not others. They could tie the invitations to T1-4 raid activity, so that people will still keep raiding in order to have a greater shot at more EX invitations. And these EX raids could have a catch rate that is a little higher than current legendaries, but lower than the almost-guaranteed Mewtwo catch rate, say, a base of 4%. As I envision it, if this were the only legendary raid system, almost every active trainer would have received one or more EX passes by now, and most would have received several, but very few people would have every legendary. Maybe I'd have a Zapdos, Entei, and Ho-Oh, and I'd be missing all the others, but everybody else would be missing a bunch too, and people would have greater appreciation for the legendaries they do have. Even having a Suicune would be a source of pride if not everyone had one. They could make Mewtwo especially rare by way of RNG, and there would still be a lot of people without a Mewtwo, but there would be less animosity about it, both towards other trainers, and towards Niantic. If a trainer couldn't make it to his EX Raid, he'd be bummed out, but at least he'd know he was likely to get another one soon, and it wouldn't be as tragic as missing an EX Raid is now..
As I see it, the problem is not so much the EX system (and the resulting fact that a lot of people don't yet have a Mewtwo), but the current regular legendary raid system that makes everyone believe they are entitled to one or more high-IV copies of every single legendary.