You're over praising the Witcher 3 greatly. I recently finished playing it and even about a week back was trudging through the remaining side quests & monster contracts (which are basically all the same). I use Witcher 3 / AC:O as examples because honestly those games share more in common with MEA than they do the original trilogy from a gameplay perspective. AC:O certainly is a very refined game. The same can't be said for Witcher 3. AC:O's problem is a shallow story with dozens upon dozens of distracting side quests that are too similar to each other and add nothing to the story. It gets tedious very quickly. When the story picks up the game is interesting, but the story is so underdeveloped and sparse. Witcher 3 is similar. The game runs off on tangents that add no real substance to the story. Those few moments the story gets back on track it is somewhat interesting. The problem is in an 80 hour play through maybe 20-25 hours actually progress the story in a meaningful way.
This is where MEA is superior to the above two games when it comes to story cohesion. Even with a number of trash side quests, many typically relate to the story in some way. The story ratio is still maybe 60%, with even the crappy side quests relating slightly. AC:O is around 50%. Witcher 3 even worse than that. While pretty crappy overall, the story in MEA actually ended and it felt like something was accomplished at the end. AC:O did a decent job here as well; too bad there was some much filler content. Witcher 3's ending was horrible. Story: Find girl. She finds you. Find another girl. Busy work, fetch quests, press eagle vision and follow tracks in 100+ quests. Some story here and there but not much. Something something super elves, portals. End game. 5 minute ending cut scene. Yeah, for 80 hours of gameplay getting a lackluster ending mission and a 5 minute cut scene was a slap in the face. MEA from the get go at least provided decent issues to care about. Figure out what happened, rid the threat, and gradually establish civilization. Witcher 3 essentially revolved around the story making you find the ashen haired girl. There is no reason to really care about this problem. We don't know who she is or have any reason to care about her other than the game outright telling you "Geralt is like a father figure to her and therefore you must care!". It made for a shallow plot with no real incentives to naturally grab interest for the player. I felt more relation to Roche because at least by the Witcher 3 I have some reason to care about his existence throughout encounters of Witcher 2.
It is a big problem in an age of increasingly drawn out and long winded copy/paste open world games. What made Mass Effect 1-3 great is they cut out the nonsense. MEA decided to add more crap and then botched the release due to quality control issues. Still an okay game, and compared to similar games it is pretty decent. As another poster said, it is more of a reflection of the state of the industry.
Alright! I can see where you're coming from in that sense. You are looking for a more 'focused' story/game progression.
But I'll disagree on for example what you've said about ME1-3. Those games offered TONS of non-related side quests. The only constant was doing them with your team of characters, and how well those characters were designed, each and every one had a very unique background and purpose. Did you forget spending hours on the galaxy map and in a Mako? Did you forget about all those DLC? ME2's entire system of side quests were essentially unrelated to the main story. Very few of that content had any business with Collectors, it was about the team members themselves. You could defend it is 'related' because building the team is what you do in this game, but the team is only a tool to achieve a goal; hell you can even have
random members die every playthrough!
ME:A and cohesion though? 'You've ended up in Andromeda' 'Now find some crashed ships'. That is the story. It doesn't get deeper than that. And about halfway through the game 'You have a nemesis'... wow.. Just wow. I've viewed literally every story progression in MEA as an actual 'side quest' in terms of how it told a story. It wasn't interesting. You knew from day one you'd once again gather up a team, get some levels, and destroy some ancient or dormant alien race. And that's all she wrote... Supported by badly written dialogue. So yes, 'more focused'.... but horribly executed. One could also say it just lacks content, because really, there isn't much to do if you don't want to walk past all the markers on a map.
My approach to these games is very different from yours. Yes, storyline matters. But immersion is where its really at. That is also how I can still enjoy a shit narrative as ME:A had on offer and still play it through. Immersion in the setting, 'being' that protagonist, making choices that somehow support that idea. Unfortunately, even in the immersion bit ME:A doesn't shine. You do some very silly way of capturing planets by 'making them habitable'... which does not really compute in any logical sense whatsoever. You call that 'related to story'? I say its a weak excuse to put five or six maps in a game.
But the premise of both TW3 and ME:A is actually the same: find (back) important people to progress the story. And its (side) quests serve to paint a canvas upon which that story happens, really. In TW3, terms of immersion, every single side quest adds to it, either in exploring playstyles or getting deeper into Witcher lore. Thát is the value of them. In ME:A, its just a bunch of events that get fed to quest logs and markers on your map.
I think you're also missing that TW3 is an open-world game in its purest form while ME:A is a much more condensed, much smaller game with more linearity. Even on the maps themselves: if you follow a route past all the markers, you won't miss a thing. In TW3, that just isn't happening, you run into high level enemies and impossible challenges. ME1-3 are even móre linear, in fact they are completely different concepts. I don't see this as a 'big' problem, actually, and I think many do prefer an open, non-linear approach to how games are made. So the focus of the story does suffer a bit, but to me that is an easy trade off. My problem with ME:A is that it doesn't do either one well, actually, its mediocre on all counts; lacking the freedom and depth of TW3, and lacking the focus of ME1-3...
Also get mods you like from ME Andromeda Nexus Mods. There are some idiocies like very small storage and you basically have to circle between map and merchants just to dump junk. Without bunch of mods Andromeda is a mediocre experience.