What you said - and continue saying in the post I am currently replying to, - is "it's preferable to first resolve your issues before entering a relationship".
But as already mentioned, you are never comprehensively "resolving your issues", unless you stop with any self-criticism. It's an endless process. Even if you succeed with fixing something about you that you don't like, to a degree - which is far from a given, - you will always be imperfect, and will always have things to work on.
Again, you are taking it my argument in an extreme way. You take it as if I'm saying you need to work until you become "perfect" human being without any issue whatsoever, 100% confident and everything. No, that's not my argument. My argument is, when you're someone like Yukiya, who considers himself lacking and thus he has low self worth that he's down about, that he keeps making comparison between himself and someone else, here Miku or even the dude hitting on her and he felt threatened by, then it's logical course to work on yourself, up until you are comfortable with yourself. By comfortable, I don't mean pursuing an endless road of self perfection or whatever, but simply resolving the many issues that make you feel so worthless.
How her relationship with Yukiya is going aptly demonstrates that rather than "striving to better herself and succeeding", as if she's reached some predefined endpoint, she still has lots of work cut out for her in what comes to interpersonal interactions.
I don't get what you are trying to say here. Miku can continue to improve herself, so? But in contrast to Yukiya, she's enjoying herself, making friends, and she doesn't feel down lacking sociability (in society, being sociable is valued, shocker I know). The one thing she feels down about, is not being cute enough for Yukiya and she fears she may lose him over this. Talk about a non issue, considering Yukiya is so into her and his lack of social skills make him unable to go after girls anyway (and he seems pretty much invisible in general IIRC so Miku is the only girl pinning after him) but hey, the manga is very vanilla, FMC is loyal to MC, there is no threat of "NTR".
The guy was 100% obviously hitting on her, which was absolutely evident to Miku and Yakiya both - and which is why she turned him down. So if anything, Yakiya had every reason to worry - actually, an obligation to worry, as he had promised Miku as much.
It's more telling of a lack of confidence, he fears Miku fall for the dude who has the qualities which Yukiya lacks, even though it's been obvious at this point Miku has feelings for him and they even play a fake boyfriend/girlfriend game to make the other confess first. If Yukiya wasn't the loner trope, just a normal guy, he wouldn't be worried over this, in fact, he would be already in relation with Miku.
Or perhaps his self-esteem issues soften in a loving relationship, as such things tend to.
If soften you mean not addressing them and they simply enjoy their relation ... until Yukiya's insecurities rear its ugly head. Miku is not going to stop talking to people, among whom are boys. We've already seen Yukiya getting jealous, thankfully he only "trash talked" in his mind, but who knows what can happen when you get emotional.
Risk what? A potential relationship with a girl in love with him, which he is sure to ruin by denying her or dawdling? You miss 100% shots you do not take, and no one in the world is going to put their lives on pause to wait as you try to set your head straight (potentially never succeeding at that, to begin with, mind).
You admit as much yourself three lines below - so what's the risk, exactly, if one option gives a chance of success, while the other is a guaranteed failure?
Letting his insecurities destroy the relation between them. What he finds lacking in himself would make Miku change her view of him, that she finds him boring in the end. Since his fears stem from not being "good enough", then he should work on himself, as it won't go away even being in relationship. Does that mean he risk losing Miku to someone else because she had enough waiting for him? Yes, absolutely. In exchange however, he'd gain more as a person. He is going to gain a good mentality, confidence, purpose and being sociable to make friends or girlfriends. Like I said, because he didn't learn to be sociable, it narrows his vision to only Miku, whom he has feelings for, yes, but also the only he can get as girlfriend. But if he works on himself, he'd see the world is larger than just Miku.
Oh, he just has to make a bit of an effort and become sociable. A couple weeks will do for a trivial task like that.
Man, if that was so trivial, why would we have people being sociably awkward even when they're adult?
Right, cause losing a girl they're in love with will certainly not affect him in any way. Neither hamper any progress he might be making in changing himself.
Sure, it would certainly affect him. But no one died from first love not working out (whether it is unrequited or you entered in couple but broke up). Most people find another. But he has everything else to gain on improving himself. It's truly a worthwhile course to take for someone with low self-esteem.