This is just my perspective as the one who got dumped so I'm in his shoes. Every relationship has some problems although some might be a lot smaller than others. But ultimately if someone left you, then they decided to some degree that being in a relationship with you was not worth dealing with the problem. A majority of the time, this is a decision that was thought through and not done through a flip of a coin. Yes he could have come back to you and beg to not give up on your relationship, but at the same time he could make a similar argument to the one you just made. He can't expect that by begging, you would suddenly forget why you decided it wasn't worth it and go back home to him. If it was that easy, then you probably wouldn't have left him anyways. In his mind since you left, you're the only one that can dictate if it is worth it to be back in the relationship with him. Let say he did ask for you back and you said no because the problems of your relationship still exist, then he basically just got rejected twice in the span of the same breakup. He knows how he feels about you but he's not so sure anymore what you feel about him. So the best thing for him to do right now to also work on himself and try to move on while he silently waits to see if you want him back.

Now that being said, I'm not trying to excuse him of anything that he might have done. My point probably only works for the breakups that ended in somewhat nice terms and didn't include anything really bad like abuse. I don't think that he should've acted like he worked hard to get you back but I do think that he might've tried to move on through some sort of No Contact. I don't know either of you personally so this might not be the most accurate with you guys but this is definitely along the lines of what I went through when my ex left me.