As a Principle: Yes.
However, the Level of Choice a Game like Life is Strange presents is really only possible in a Game like Life is Strange. That same level in a Game like Mass Effect, especially if the Storyline plays out over more than one Game without "soft Reboot" like going to Andromeda, would weigh down the game immensely and override other Aspects of the game - which Mass Effect actually has, unlike Life is Strange where there's really only the Story built from your Choices and their Consequences.
Your later Idea, having most Choices be localized and bound to Characters instead of Civilizations seems to be the smarter Way to go about this. In Retrospective, this is mostly how Mass Effect 2 did it, where there are very few Galaxy altering Choices, instead focusing on the Characters, especially your Squadmates. Mass Effect 1 was a great Game, but the big Choices in that Game presented a Problem later on in Mass Effect 3 (where I think Galaxy altering Choices where absolutely okay to be placed, as it presented a Conclusion, however it turned out). In the End, most of the bigger Choices from the previous Games and even the same Game lacked Impact upon the actual Outcome.
I think, comparing Life is Strange to Mass Effect in Terms of Choice and Consequence is only possible when taking it with a Grain of Salt, as basically ALL Choices in Life is Strange are Character-based. It operates on a infinitely smaller Scale than Mass Effect and I don't think it would hold up much better under the Pressure of several radically World-altering Choices than Mass Effect, which effectively collapsed under them, reducing them to a Number that didn't satisfy anyone. So in the End, I do think, there should be more Choice and Consequence in ME:A than in the other Mass Effect Games BUT this should go hand in hand with a dramatic Reduction of world-altering Choices, maybe even to only one per Game, preferably the "big" Ending Choice (Dealing with the Council / Collector-Base / RGB).
Instead, the Choices should mostly operate on a smaller Level like "When Character X says What Why". On this Level, I think, the Writers should be invited to build in much more Complexity. This could also serve to allow the Player Character for more personal Agency.
And, on Life is Strange... 