Blitz only helps with your time management, which clearly some people need. (One of my opponents in a 25 minute game ran out of time on move 9!) But other than that, it doesn't help you at all because you think faster, causing more mistakes. Then you think faster in slower games, causing more mistakes.
You're missing the fact that when you get common mistakes, which you always will get in blitz, you can analyse and work out how to improve your reaction. Let's say someone plays the Slav and it goes typically 1. d4 ...c6 2. c4 ...d5 3. Nf3 ...Nf6 4. Nc3 ...Bg4, now that's a main line Slav up to but not including black's fourth move, ...Bg4. Black's fourth move should lose. If it isn't a forced win, it must come very close to it and end up as a position where white has an overwhelming development initiative.
So, would you know how to win against 4. ...Bg4 in the Slav? This is just one example out of very many possibilities, where the opponent goes wrong but the answer isn't in any chess book ever written, more than likely, since the move is in the opening and it's such a bad move they don't include it.
My own coach told me that blitz is bad because you make mistakes and your opponent doesn't punish them. I'm afraid I'm gonna have to favor my coach over you. No disrespect meant.
He's inexperienced.

Blitz only helps with your time management, which clearly some people need. (One of my opponents in a 25 minute game ran out of time on move 9!) But other than that, it doesn't help you at all because you think faster, causing more mistakes. Then you think faster in slower games, causing more mistakes.
You're missing the fact that when you get common mistakes, which you always will get in blitz, you can analyse and work out how to improve your reaction. Let's say someone plays the Slav and it goes typically 1. d4 ...c6 2. c4 ...d5 3. Nf3 ...Nf6 4. Nc3 ...Bg4, now that's a main line Slav up to but not including black's fourth move, ...Bg4. Black's fourth move should lose. If it isn't a forced win, it must come very close to it and end up as a position where white has an overwhelming development initiative.
So, would you know how to win against 4. ...Bg4 in the Slav? This is just one example out of very many possibilities, where the opponent goes wrong but the answer isn't in any chess book ever written, more than likely, since the move is in the opening and it's such a bad move they don't include it.
My own coach told me that blitz is bad because you make mistakes and your opponent doesn't punish them. I'm afraid I'm gonna have to favor my coach over you. No disrespect meant.