Hmm. @CorvathraNoob I think both sides of this are correct. I'll explain from my own personal experience.
Several months ago I decided to get into playing ladder. I was around ~900 ladder rating at the time iirc, which was massively underrated for me so I was winning basically every game even though each game I knew I was making massive and obvious mistakes. As long as I was able to leave each game knowing the huge mistakes I was making, I didn't bother watching the replay. I'm certainly not at the level of Arch or Turin for instance but my game knowledge and skill is still far better than a 900 rated ladder player's game knowledge, even at this time. I basically was just needing to get my muscle memory up to par with that in a game mode I never really played while coming from being mostly a Setoner.
I very quickly improved and I stopped making as many mistakes that were glaringly obvious to me in game. Up until I got up to about ~1300 ladder I basically didn't lose any games other than some purely cheesy cancer ones where I didn't adapt well or ones where I just completely messed up something basic for whatever reason - usually me first timing a map and not reading it correctly vs someone who played the map a lot.
Around this time I ran into a problem. I was still making glaringly obvious mistakes that I recognized in game, but the issue is that these mistakes were getting harder for me to fix. Things like general map awareness, spending apm on the right things, not over/under ecoing (huge one for me atm, but I digress), and misreading new maps are all mistakes I was easily able to recognize in game but have proven hard for me to fix. These are muscle memory flaws I have and need to address. While I work on these though there are a thousand other flaws in my gameplay that I can address. But at this point I have to watch replays to actually address them.
A lot of those things I mentioned, and the thousand more things plaguing my gameplay, are all things that have a bunch of tiny components that watching replays now all helps me improve on. Yes I know in game I'm making mistakes, I'm actually frustratingly good at recognizing mistakes in game at this point. It's a bit depressing to play knowing I'm playing like pure shit every game but I'm digressing again. The issue is often times these mistakes are things that happened before I recognized them. They often are coming about from different sources than what I realized. Watching replays helps me with this. This long winded rant now brings me to my point.
If you're able to leave the game with an immediate, obvious, and small thing you can do better in the future and quickly improve on, then watching the replay might not be that helpful while you work on that. If the main errors you're seeing are more nebulous and take reworking your muscle memory and a lot of time and effort, then it's important to watch replays so you can keep making the smaller improvements while working on the big stuff that'll take time and experience.
TL;DR: In my opinion people on both sides of this are correct, depending on which stage of ladder experience the player is in. If you can make easy and obvious improvements each game then watching replays might just take time away from making those improvements, if not then watching replays is important.
Edit: I am also coming from the perspective of someone who has played Supcom on and off since the first one came out in 2007. When I got into ladder earlier this year I had far more experience and game knowledge to call on than someone who is relatively new. A new player doesn't have this advantage, and therefore will most likely need to spend more time watching replays earlier on.
Edit part 2: Thought I'd give some more specific examples to illustrate my point using my comment about over/under ecoing. The over ecoing part isn't surprising to either myself or anyone who knows me: I'm a Setoner and ecoing is the name of the game there usually. The under ecoing is the more interesting one. One big reason that it happens is because I know I have a tendency to over eco, so I intentionally just try to make more and more units without ecoing to compensate - often times I'll go overboard there. However, outside of previous tendencies there were some glaring mistakes I was making leading to this happening that I had to use replays to discover. Lots of components here but the two big ones are: my early expansion was far too slow leading to me having less mass than I should early on, and two is that I didn't have enough engineers in the right places to get reclaim. I still have a lot of work to do, but I don't think I would have realized just how pathetically slow my expansion still was and that I was misplacing engineers as quickly as I did without replays. I knew the overall mistake, messing up eco, but couldn't identify all the components of it without replays.