The main reason I enjoy the distinction as a player is so that I can advance the main plot at my own pace.
Strictly speaking, if I'm playing a game and enjoying it, I want to do as much of the content as possible. Most games "end" when you complete the main story missions. Granted, some will tell you, "Hey, this is the point of no return, go do anything else you haven't done and come back", but that always feels like a "slap in the face" to me as a player. I much prefer the game just say, "Hey, this is the main story quest, do this to get closer to the end of your playtime" and "hey, these are sidequests that only matter if you care about doing them".
This approach lets me choose which content I want to interact with and which I don't. Granted, I usually do absolutely everything, but there are cases where I just don't care about a quest and would rather I skip it.
New Vegas had this issue for me. Well, okay, one of many issues that game has... it's a literal garbage fire on any close inspection, but this is one of the major issues that stuck out to me as a player.
Namely, nothing really felt that important in New Vegas. The game didn't properly set up that it was even remotely important I be chasing Benny to begin with. Granted, if you go to Primm or whatever and view a very specific terminal that tells you about Couriers, you realize why you might have a motivation to go kill Benny and get your cargo back... But... Beyond that, the game gives you nothing. Because each quest was just "a quest", none of them felt important or impactful. More importantly, they sort of robbed me of my agency a little. Sometimes a random quest I completed would tie into another quest or part of the main story quest and I'd find that out much later. I enjoyed working with the Boomers and wanted to live with them and such on my first run, but then the game informs me that they're "flyover country". They exist purely to serve the main story and for no other reason. This shifted the context of their quests. I was no longer doing them because I enjoyed hanging out with them and liked their philosophy. No, I had been shmoozing them to get access to their guns and a plane that they could use in the Final Battle... as well as access to a few useful items you would want for the Main Story Quest.
New Vegas literally gives new context to some of your quests once it tells you that "Hey, this is part of the Main Story Quest, and you already did it, so move along". Interacting with the Boomers suddenly felt cheap and hollow after the game told me that. It was no longer, "Hey, I helped these people because I like them" it was, "Hey, I helped these people because the game suggest at some point I do so as part of most of the endings of the game". Interacting with them was a foregone conclusion. It wasn't some "out of the way" place I found with cool people that I worked my way into the good graces of. Oh no, I was always MEANT to come here. I was always MEANT to interact with them.
New Vegas had this problem a lot.
Well, it did also have a separate problem in that when it gave you quests, it didn't really tell you WHY you should be doing them. I picked up a lot of quests and did them purely because an achievement existed. Or, I wanted to level up. I didn't want to chase Benny down. I didn't care about the stupid cargo I was carrying. The game makes no big deal of me being a courier, and I never carry anything for anyone again, so my job is just a plot excuse. The game never punishes me for losing the cargo. The game doesn't reward me for getting it back. I didn't even want to kill Benny. Heck, I didn't even want to get involved in the stupid localized conflict of the area. If I did get involved in the conflict, I wanted to be the one in charge of it all when the dust settled, but there was no option for that ending. I could be a mean and ruthless and terrible jerk in the game... and I was still forced to play second-fiddle to other people and it would be an "ultimately altruistic" character I was playing by the end credits.
That's sort of the problem when you just have "Quests". Anything to do with the main story feels like, "eh, just something to do" until suddenly the game is over. Likewise, the message of your "main plot" essentially gets destroyed, as do the themes of your game. New Vegas liked to paint Caesar's Legion as some massive force of terror and elite warriors who posed a serious threat. But, every interaction I had with them didn't paint them that way. Every quest to do with them didn't make me think of them that way. Most of my interactions with "the main threat" were, "do I really have to fight these guys again? They've got garbage loot. How're they a threat? How do they manage to kill ANYONE in the wasteland when nearly everyone is packing heat? How are they any sort of major threat at all?"
Without the title of "Main Story Quest" to push me along, I just had no motivation to do many of the quests beyond, "get loot, get levels". Then, in the rare instances where I found I cared about something in the game, it retroactively ruined it for me by telling me, "Oh hey, you skipped part of the main story quest here, so you don't have to do it now, here's the next set of objectives".
Heck, in New Vegas I ran into quests like, "provide power to the Mohave" that I did because it felt important to do. I was like, "Yeah, that sounds cool, let's get some power flowing here, get some more amenities". What was the main story quest at the time? "Chase down a guy who stole a poker chip from you".
You seriously risk making your main story less important than side content if you just treat all quests exactly the same.