What is the rationale behind Black playing e6 in so many openings? I am new to this stack exchange, so apologies if this question doesn't fit here.

Though I have advanced through the game, and now have a somewhat respectable rapid rating of 1550, I have always found some chess openings to be a source of confusion. At present, I play the Slav (proper) against 1 d4, and the Caro-Kann against 1 e4. Many other respected defences don't make sense to me. For example, the French defense has a similar idea to the Caro-Kann in that Black is trying to counter-attack in the centre rather than directly preventing White from playing 2 d4. However, the 'problem child' of the French defense has always been the light-squared bishop. Granted, 1... e6 allows Black to develop the dark-squared bishop on the second move, but this seems to be outweighed by the fact that the problem with the light-squared bishop can persist for a considerable portion of the game. And yet, 1... e6 is more popular than 1... c6, and is at least as theoretically sound. Why is this? The same could be said of the Semi-Slav, which again is more popular than the Slav defense. These moves never seem to be explained by chess authors, and yet they seem to violate opening principles.
In the French Defense, the modest pawn advance in e6 simply plans to challenge the e4-pawn by d5, without having to recapture with the Queen after a possible capture in d5. The idea is thus similar to the Caro-Kann. The differences are that the Caro-Kann takes away the best square for the b8-Knight, while the French blocks the natural diagonal for developing the c8-bishop. So there is a trade-off but both openings are safe and solid methods against 1.e4.

The idea of e6 in the Semi-Slav is also to reinforce the control in d5 and take back with a pawn if White plays cxd5. It's true that the c8-bishop is blocked but Black can solve this by either taking in c4, followed by b5 and Bb7, or by playing b6.