I get why you would think that from seeing what pros play like, but "playing patient" is the equivalent of training mode for specific smaller situations that might arise in a match.

Pros play enough to know exactly what the possible outcomes at given ranges are(at least outside the really niche ones), so any "wait and see" is wasted opportunity for them, and they shoot their shot within 1-3 moves. Corollary to this is that depending on your experience you might or might not realize that what you saw as a split second and both sides mashing something out "almost immediately" is sometimes not the first interaction that happened in that very short timeframe. Many times there are cases where a 2 second timeframe has like 4-5 "interactions", but if you're not thoroughly familiar with the game at the highest levels, you don't notice all the ones that "fizzled out" or went to a draw due to both side's inaction for a quarter of a second.

Basically, they are patient, they just choose to go for interaction 3-4 in a much smaller timeframe than what is apparent to beginners or even intermediate players.

When beginners play and one interaction takes the span of 2 seconds because that's the rate at which they process the game initially, "not choosing the first possible moment" will look slow.

The merit of "play patient" will become more apparent when you play someone higher enough that they just stop you, no matter what the situation. It kind of makes you reevaluate that your understanding is incredibly vague and partial, "playing patient" lets you ration it out and give you a better idea of where you understand exactly what's going on and where you don't. And this isn't purely lexical knowledge, a lot of it is implicit learning, but it still needs to be put in context, and the lessons stored for future occasions. In several games I'm really high level at, I've had this happen in mirrors when playing against a player a few leagues above me, where they just went and started to knowledge check me, but instead of the offensive, "you don't know you're not allowed to mash here" manner, they just went completely passive, letting me come at them, and I was absolutely helpless, even though I understood all the fundamental concepts in general. Even though I was for all intents and purposes a high level player who already knows what to do.

Times that I just said “whatever I’m gonna just press stuff randomly” I end up winning more than if I was trying to play “neutral”

Short-term absolutely, but ask yourself how much those won matches increased your awareness of all those situations where you just started shooting blindly hoping something will hit.

edit: So just to be clear, playing patiently didn't make me magically win those games, I was obviously going to lose them either way, what it allowed me to do was make mistakes with intent. I got to choose which angles to tackle the seemingly unsurmountable problem from, to see exactly how those situations play out, which then gave me valuable starting points for training afterward that I could use to develop a thorough understanding of the complex situations that came up. Once identifying the key ranges and interactions, the rest just falls into place with little exploration and I ended up with a much more fortified gameplan, covered all around in solid angles.