I think a lot of men aren't really presented with their definition of a "perfect woman," and I don't think it has anything to do with looks. Romantically speaking, I'd say that looks do play a part but they're not the most important part. Men need to feel appreciated, and in my own personal experience, I feel like a convenience at best and in the way at worst. Don't get me wrong, there are some women who do genuinely care, but a decent number of them don't really seem to care about what makes a guy tick, what drives him, inspires him, what pulls him back from the edge and all the internal defining traits that make us unique. I honestly can't even remember the last time I felt like a woman was actually trying to understand me. Men try to understand women all the time because I think a lot of us do really want that romantic and special connection with just one person. Ironically, I typically find that the opposite of your post happens. I often hear women talking about their perfect guy and listing all the parameters they have to meet before they would even "earn the right to speak to them" (not even using hyperbole for that quote). I'm sure that there definitely are some men out there that only want the best looking women, but from my experience, men really just want someone who actually cares about them and continuously shows it. It sounds straightforward, but it's scarily rare for some guys these days. It's possible that this phenomenon may have even had an effect on some guys that's made them go back to their old ways of treating intimacy like it doesn't matter and not giving the potential of relationships any credit.
In saying all of this, this isn't an accusation against women or blaming women. It's simply an acknowledgement of circumstance.
Either way, looks do matter in a relationship and I'm pretty sure it's something that's been used as a deal breaker for me not getting into relationships I've sought after in the past. However I think that there's a big disconnect between what the opposite sex actually wants and what the other sex thinks they want. The main problem is communication. If everyone was more open to what other people's opinions and personal experiences were, I'd say we'd all get along much better.
Apologies for the length, but I had a bit to say on this topic.