A counter argument is that an alphamale will see a girl that he wants, and will just go up and assume the sell. This can also work, if you genuinely come across that way, and if you have the followup to back it up congruently.
Generally though, this is uncommon. Natural PUAs generally just walk around, and girls give them AIs (approach invitations) or make it really easy for them by throwing themselves at them, in a way that most surrounding men just don't recognize (and women don't acknowledge, as this would be a breach of "Secret Society" to admit what's happening, and would break down their whole system of secretly being the CHOOSERS). Note, that the idea of the alphamale who does approaches in society is a SOCIAL MISCONCEPTION. This rarely happens. Generally, natural alphamales do not do cold approaches. I've travelled all over North America and Europe, and I rarely see it. I know exactly what to look for - and I *rarely* see them initiating cold approaches. It happens only in certain communities, like London and NYC. But this is very very uncommon, and even in these communities 99% of the naturals who get laid often are still not doing cold approaches.
The ideas that "men take all the risks in escalation" and "men do the approaching, women do the receiving", that the academic community of psychologists and zoologists have espoused is BAD DATA. It is literally a fallacy and blemish of the academic community. It is a pathetic and glaring example of the follies of academia's white ivory tower armchair theorism, from eggheads who couldn't put any of their theory into practice if you gave them 10 years of prepare it (this is a gripe that I have as a student of political and analytic philosophy, that I see transferred over into this field as well). What these social scientists don't see (AFCs that they are), while they're watching all of the interactions that they supposedly use as empirical data in their published studies (which influence social understandings and thus social conditioning), is that while the men are the ones approaching and escalating, it is the women who are throwing themselves at these clueless men, until they do something. So in that case, the woman has virtually ALREADY DECIDED that she wants the man, and from there she just doesn't admit it (secret society breach), but rather throws herself at the guy until he escalates. She even puts up silly shit tests like (this from a double lay that SB007 and I did on a 2set that we pulled) "Just because you're renting that hotel, doesn't mean we're going up with you."... and later on in the night .... "just because we came up here, doesn't mean we're sleeping with you.." And typical AFCs, will say "Wow, we really plowed through that resistance", when in fact these girls had chosen to sleep with SB007 and I LONG before we'd taken them back to the hotel that we rented right in front of them. We were the hard to get guys, and just let them play out their dramatic act of throwing themselves at us in subtle ways, while pretending that they didn't know what was happening. And then we allowed them to structure the extraction while making it look like it was our idea and not their fault, and then afterwards they denied responsibility for what took place, while they still email us regularly and want to meet up again. These girls would claim that we chose them, when in fact they chose us - which few people realize is the way it almost always happens.
The idea that "girls choose" also stems from the male/female social dynamic in our society, and the practices and habits that spawn from it. Men are unconsciously giving sexual validation to attractive women all day long, in one way or another. It's either they're checking them out, asking them the time, trying to make small talk, or pivoting left instead of right as they walk out of a room - when it would be faster to pivot left but he can catch a glimpse of her by pivoting right. Girls are all too aware of this stuff. It's built into them. They also go to the club religiously, to relish the process of guys buying them drinks and checking them out, and then shooting them down. A quote over from literally the hottest girl on my campus two months ago after an off-night: "I'm so depressed. No guys approached me tonight. I would never get together with a guy from a club, but I can't believe that I didn't get approached."
