Something that always bothers me in these discussion about fetch/side quests is this constant concept that you could swap one for the other. The fetch quests, by nature, require only a minimal resource cost and even if they removed them from the game, it is very unlikely that there would be anything that would be in the game because that decision. For example, the Varren meat example given above sounds like a pretty resource heavy sidequest for something that is essentially a fetch quest. So the discussion should be framed do fetch quest do more damage than good rather than should we have immersive side quests instead. Because those two things are completely irrelevant of each other.
Also, I can never really wrap my mind around the constant use of ME3 as the bad example here of side quests. ME3 probably has, on average, the most expansive and intricate side quests Bioware has done, with the possible exception of DA2, yet they are apparently considered so good that they can't be really considered side quests leading to the complaints about the fetch quests. Which, as already pointed out, are a really small part of the game. And while it can be debated, I think I understood why they wanted those quests to be overheard instead of getting them from Central command as this way the player heard the context for from people it affected. You heard the Volus merchant beseeching the lost values of his people, you heard the Batarian preacher urging his people to continue to be strong. Compare that to just getting a message from SPECTRE control about how it would be great to get those pillars back. Implementation can be dicussed, but the context of the decision is also important to be noted.
And even with those, while I will freely admit that subjective experience matters, it is pretty much the same thing that ME1 and ME2 did. ME2 literally had overheard missions on both Ilium and Citadel. In addition most of the fabled side quests was Shepard flying in to a system and randomly stumbling over something happening. Yet it is constantly used as a golden standard of side quest design here. As for ME1, even ignoring the exhausting fetch quest system it had implementd, here are some of the side quests from ME1: Walk past a random people and end up deciding a fundamental healthcare question for them. Walk by a random admiral and suddenly get involved in Cerberus plot. Walk on the Citadel and end up deciding where a Hanar preacher is able to act. Walk by a random waitress and get involved in a deep level infiltration operation. How exactly are those functionally different in hearing that someone want something?