When you consider that, it's not just self-reflections, he's making active progress, just not as fast as people would like. (Humans are not patient by nature. Not really.)
If that's not enough, then ignore that. Let's consider the the time instead. Each situation lasts for several chapters (longer than your typical manga's pattern) and some ever overlap each other making it feel longer. Probably 5 or 6 months has passed. Not a year (not by a long shot!). For an aggressive guy (I don't subscribe to the whole "alpha" "beta" bullcrap. That's middle school frat boy ego-stroking nonsense) brimming with confidence and pursuing a girl and ignoring Ruka or other girls after him, yeah, this is unacceptably long. But most guys like this are typically "hit it and quit it" too (keyword is MOST, not ALL). Passive guys are more failure prone and prefer taking a more calculated and "safe" approach. The less risk, the better, because they are done being hurt (evidenced by our MC here). To take 5-6 months getting to know the girl and dating her, this is actually normal. The only real argument is that they're not really "dating" due to the whole Rental thing (One could argue they are due to Mizuhara's tsun-nature and using it as a pre-tense, but another can say they aren't because she's been a professional about it and not real girlfriend. Readers could argue this point forever!).
Anyway, just saying there's more to it than his "spineless" nature. Not saying you're wrong, because you're not (it was very well put, by the way!). Anyway, just my opinion, so take it with a grain of salt.