Me too. I have the "old" versions "Mass Effect 2007", "Mass Effect 2 2010" and "Mass Effect 2 (2010) Edition" (for some reasons there are two versions of old ME2) on Steam and was about to buy Legendary Edition and finally getting started to play. But I'm not happy with the additional requirements of it, as it requires Origin client and an EA account to play this single player game. This is unacceptable to me. Old versions do not require this.
So after my research and being confused of multiple versions and if the Legendary Edition is worth it, lost interest. But ME2 is still on my list to play soon.
You can mod the first three to get it close to par with the Legendary edition. The improvements they made in LE on all 3 make it worth playing, but if a user account is your limit I guess not. There are a ton of mods for LE now as well.
I play most PC games without modding, especially because I'm on Linux. I've compared and read about the improvements, and to its just minimal changes. Only the first game got huge improvements, but I'm more interested into playing 2 only. And as someone playing lot of old games and emulate old systems, its totally fine with me. I even played GTA 4 (last year and this) without modding on PC, but still have to finish it.