Is trading a knight for a bishop (or vice versa) worth it anyway?

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Sometimes.

Usually bishops are better than knight, at least thats how the masters treat it. But knights can be tricky to handle for lower level players. For lower level players whats more important is understanding how good or bad the piece is, you might want to give away your bishop looking into the opponents pawn chain for a knight, for example. 

depends usually on the position

All those that oppose me shall drown in the blood ov their kind. Kill them all, revive them then kill them AGAIN.

A bishop 3.33 P is worth more than a knight 3.05 P.
Table 6
https://arxiv.org/pdf/2009.04374.pdf 

You can't just put arbitrary absolute values on pieces, thats not how chess works. every different position will have different values for different pieces. a well placed knight in a locked closed position is far superior to a bishop

I mean, the bishop is worth more because it’s usually better in most positions, with it’s better maneuverability and scope and all. Just like how a queen is worth more than a pawn in most positions, but if you’re getting mated, the pawn is far superior. You have to look at the position and be the judge.

It can be. Ruin pawnstructure, winning pawns, opening up the position in your favour, going in to a winning endgame etc.

A knight can attack two colors where a bishop can attack one so if you have an endgame where you play knight vs bishop and have every pawn on opposite colors of his bishop it would mean that only his king can attack your pawns. 

#8
"You can't just put arbitrary absolute values on pieces"
++ That is not arbitrary, it is based on 700,000 games.

"a well placed knight in a locked closed position is far superior to a bishop"
++ That is right, but a knight is in some positions superior to a rook or even to a queen.
You should look at BxN as a sacrifice of the minor exchange, like you see RxN as a sacrifice of the exchange and QxN as a queen sacrifice.

Right, you're proving my point, a knight in a position has the potential to be more valuable than even a queen, so you can't just put an absolute value on a piece, regardless of. 700,000 game sample size. That sample could represent low level games, high level games, unorthodox openings, engine analysis, etc. The value of pieces depends on its current position on the board and its potential for use on the board. 

It makes no sense to look at a Bishop for knight exchange as a sacrifice because it's not, they're both equal to 3 points held in your hand, and in any given position giving the knight for a bishop could be an exchange sacrifice. 

#12
"they're both equal to 3 points held in your hand"
++ No, they are not. The bishop 3.33 is worth more than the knight 3.05.

Depends on the situation. I believe it can generally be summed up in two scenarios:
1. In semi-open or open positions, typically trading bishop for knight is not the best idea (especially if that means opponent obtains bishop pair)

2. In closed positions, trading bishop for knight is not necessarily a bad trade, but once again, depends on the specifics.

But yes, typically at the beginning of the game a knight for bishop trade is favorable.

#15
The results of AlphaZero only confirm what human world champions Kasparov, Fischer, Capablanca, Lasker, Steinitz have said before: the bishop is generally worth more than the knight. The difference in worth is about the value of 1 tempo i.e. 0.33 pawn.
There are exceptions where the knight is stronger than a bishop, stronger than a rook, or even stronger than a queen.
You should look at BxN as a sacrifice of the minor exchange, like RxN is a sacrifice of the exchange and QxN is a queen sacrifice.