I wasn't trying to find a mate but I ended up meeting my current and likely life-partner during a particularly "stoic" time of my life where I had decided to stop trying so hard to make other people happy and focus on my own goals. I didn't stop holding the door open for ladies, or anyone passing through with or behind me, but I did re-align my career and life focus.

Since I wasn't trying extra-hard to win and keep her as I had in previous relationships I think it allowed us to find the places where our interests truly overlapped and allowed us a much deeper connection. I ended up having two kids with her and we get along and work together great. She's more attractive than me and makes more money, so what I offer her is not superficial, but I don't know that she would have discovered that in me if I had been trying hard to amplify those superficial attributes.

So I think there is something to be said for pulling back a bit on pulling out the chairs and paying all the bills but not for the same reasons you seem to think so. Also, I think many women are rightly cautious about a potential mate who seems to be trying too hard.