1. e4 c6 2. d4 d5 3. e5 Bf5 4. Bd3?! Bxd3 5. Qxd3 e6

Yes, it has been know Bd3 is a lame move for a long time. Not sure necessary to play e6, chould play Qb6 then Qa6.

I don't think 4.Bd3 can be legitimately dismissed in such a cavalier manner. "...white is simply worse"??? Come on. You call that analysis? The above comments are overly simplistic, given the complex possibilities of chess. This variation bears deeper analysis. That is what I've been looking for online and have not been able to find it. More work needs to be done on the variation. 

If you want to do the work then do it. You can start looking at the Nimzowitch v Capablanca game(s).

kasparov among others, who even played that same caro-kann as black

If you aren't going to give a definite answer, don't answer. I've seen four of your comments on forums in the past day, and not a single one has been anything but "Depends" or "It depends". That's not useful unless you at least explain what it depends on and why. Otherwise, why bother saying anything?

@Ethan_Brollier

They are just trying to be annoying on purpose or they think it's funny. Better to not give them a reaction.

Bd3 is a lame move as it justifies black's play. Black is able to trade, play c5 and get a French without the LSBs which is essentially everything black hopes for out of the Caro-Kann. Black completely equalises.

It appears to be about +0.17 in white's favor at 35 depth on Chesstempo. Perfectly even game. Still able to defend the d pawn as well.

It doesn't matter what the engine says. From the human perspective black is getting more out of this trade than white. Black trades off the LSBs and has all their pawns on light squares. d4 can be defended but white is going to be on the backfoot and doesn't really have any plan. Black's plans are very natural.

The engine can say it's equal but the human game results paint a different picture. Out of 137 games in the master's database, black won 36% whereas white won 29%.

137 games isn't enough games for a statistical significance.

This is the master's database so we can assume the players were playing fairly well. In the lichess player's database, out of 2,463,734 games, black won 49% and white won 46%. It's technically equal but, from a practical human perspective, black has no problems and their plans are clearer. White's play is unambitious as trading off a pair of minor pieces fails to capitalise on white's space advantage and makes black's game easier.

The Short and Tal variations are much better. Even though in many lines of the Tal it's technically equal, it's a different kind of equal. The pieces are kept on the board, maintaining complications, and the play is sharper, resulting in better winning chances for white.