Playing slowly depends on the time format of the game, If you are playing a bullet time format and you play slow, then you will make very few moves and time will run out before you checkmate your opponent. If you are playing a 90mins game and you play fast, then you will probably get checkmated and spent the next 75 mins waiting for the next tournament round to start...
There are both merits and demerits of analyzing a position too much.
Consider below position
[Event "Bled-Zagreb-Belgrade Candidates (1959)"]
[Site "Bled, Zagreb & Belgrade YUG"]
[White "Robert James Fischer"]
[Black "Mikhail Tal"]
[Result "0 - 1"]
[FEN "1q2kbr1/p3rp1p/8/1p6/8/5Q2/PPP3PP/R4R1K w - - 0 1"]
1. Qc6+ (1. Rae1) *
In the above position Fischer analyzed the position for a while, and had a move that could draw the game, he even wrote the move down (This may not be the practice today) but ended up playing a different move.
Rae1 would have secured him a draw but the move he played Qc6+ cost him the game. So if he had not analyzed the game too much he would have drawn this game
I believe it is Magnus Carisen who said that sometimes he knows the move he will make but still analyzes the position even more on long games. For short games like blitz, if you know the move, make the move
Consider this position
[FEN "r5k1/5ppp/5b2/2R5/8/6P1/5PBP/6K1 b - - 0 1"]
1... Ra1+ 2. Bf1
(2. Rc1) *
Is there need to think about the next move? There are only two moves, one is just giving out a rook. If you are playing a blitz game for example and there is only one move possible, play that move
Some positions may require more analysis, consider the below position
[FEN "1r2k2r/p4ppp/2b3n1/1pRBB3/8/8/PP3PPP/5RK1 b - - 0 1"]
1... Nxe5 *
How does white continue? Depending on how complicated the position is, there may be need to spent more time.
Now what if you have too many options at your disposal?
[FEN "5r1k/ppbq1np1/2n1rp1p/8/2PP3N/2NBP3/2Q2BPP/R3R1K1 w - - 0 1"]
In a blitz game I take the 1st good option and make it but if I have time, I can think about the position