@archsimkat
This is completely incorrect. You need to do analysis of your replays regardless of your current level, and I would argue it's especially important at low levels (0-1000), where there are likely large amounts of low hanging fruit, ripe for improvement. Getting "basic routines in your blood" and not analyzing your own gameplay while you are at 0 ladder rating will serve only to ingrain the bad habits you currently have.
I'm going to agree with Zokora on this one and say that especially considering how inconvenient it is to go through FAF replays compared to SC2, in particular being incapable of rewinding or skipping through to specific parts you are interested in, it's probably more valuable for a sub-1k player to just play more games and try to focus on important things in each game. You're obviously going to make mistakes, and vitally, should notice that you made IN GAME.
How does the noob even know what they are doing well and what they need to try to improve? IF they already DO know those things, they should easily notice them in game and not even need to watch the replay. "Holy cow I'm currently stalling -300 power in this game 5 minutes in, I should adjust my build order and make more power next time!" If you know stalling is bad, you realize the mistake IN GAME and watching it again in the replay is a waste. If you never pay attention to your resources, that's an even more important mistake that also ought to be realized IN GAME. "Hmmm, all of a sudden I have 10000 mass in the bank, last time I checked I was stalling -50. I should probably glance at my resources a lot more often!" I mean this is probably the most important thing to tell noobs. Besides learning a better build order, trying to manage eco better is something you should just know is vital, and don't need to watch a replay for.
E.g. It's better to cap t2 mexes then upgrade them to t3, than to just upgrade them to t3 without capping them. How does the noob realize this when watching the replay, without being able to notice it in game? If they don't know, watching the replay won't even reveal the mistake to them!
"Basic routines" are basically acquired from copying better players. I think that's an order of magnitude more beneficial to a noob than watching their own replays. Sure, you probably won't get too much benefit from trying to copy a 2k player's bo, but just look at someone a few hundred points above and that should be easily attainable.
The only reason you might benefit from watching your own replays is if you have almost zero awareness of what is even going on in the game, both economy-wise and with your units. You can become more aware from just learning the game better and getting more familiar with it, which I think happens a lot faster from actually doing it and seeing what better players do.
@Turinturambar
How do you want to check if you actually improved on the basics as you aim to improve on? Apart from finding new issues/new tactics in replays, watching replays can also just serve as a check how well your doing on your objectives e.g. how much e/mass did you actually stall/overflow and for how long? how many factories were idle and for how long? how fast did you actually expand? how good was your agression really? how good was your scouting/intel? how many tanks did you suicide for no reason?
While playing you will likely not notice how much you failed/not failed to fullfill your improvement goals.
You can check to see if you have improved by looking at your rating change over time. Your change after just a few games or a couple days isn't important, because there will be significant variance and noise in the distribution of results, but in the long run it's an excellent, objective indicator.
All of your other points get basically the same response as I gave to arch. Yeah, you might learn some new tactics from the other noob you played that beat you, but watching significantly better players than both of you is probably more valuable. If you're 500 watch the 800-1000s play and try to imitate that, or the best players that you can actually effectively copy (so as to not ingrain bad habits, which I do agree with arch could be a problem). And it can't be that useful to watch replays to see what mistakes you made, if you can't even notice you made those mistakes IN GAME. You won't do a good job of correcting your mistakes in the future if you still haven't learned where to focus your attention and realize where those mistakes are happening in game. E.g. "Oh wow I was stalling power bad, better change my bo." Ok if you notice that in the replay, you might improve your build order, but if you still haven't learned to very closely monitor your resources, when your opponent snipes all your power with an arty drop and you don't notice you have zero power income for 5 minutes, that's an exponentially larger problem that needs to be solved FIRST. And once you have figured out "pay close attention to your resources" you no longer need to look through your replays to see if you were stalling, because you will have learned one of the most important aspects of this game, which is always paying close attention to these crucial factors IN GAME. You see you were stalling, then ALREADY KNOW to make some adjustments for next game. Watching the replay is a waste. Just go have fun and play some more games. Who knows, if you miss that next ladder game by a minute, you might not get another one for 3 hours!
Edit: my examples were economy related but the same thing would go for units. "Hmm I sent all these tanks in to this unscouted area and they all died without killing anything. That was bad." Even if you didn't see the fight and just notice the army is gone, if you see point defense where you sent tanks, you realize you might want to micro those units or watch them closer and not suicide them. Even noobs can figure out "suiciding units=bad," but what they might not even understand fully in game, or from watching their own replays, is what types of strategies are most effective. I can imagine a noob thinking, "Oh, I guess I just wasn't at critical mass of tanks, and need to send even more next time!" Where they would instead learn from watching better players that attacking t1 pd with t1 tanks is not a strong tactic.