Yes, I agree. As I said, I don't actually agree with the idea that men should take the lead and pick up women, just observing that this is how it seems to be done in both cultures. I guess more accurately, you could say that men are expected to "pursue" women (which is different from picking them up). Again, I don't really agree with this social construct: I totally made my interest clear to my now-husband. I've never been very good at holding things in and I definitely don't play coy - the downside is that this has tended to scare away guys who still adhere to the old "man chases woman" model. The upside? The guys who are left are totally down with assertive women! I'll take that trade-off! I can't say whether a Taiwanese guy would be more or less likely to be scared off by a woman who does the pursuing than a Western guy, because I've never had to find out.
That said, it's hard for most women to ignore all the social conditioning they've been given to be the pursued rather than the pursuers. We hear it from family, books ("He's Just Not That Into You"), movies, society in general, and even in Taiwan for as much as a Western guy might say that part of the problem is that we wait to be picked up, when you hear a Western guy talk about his Taiwanese girlfriend using adjectives like "sweet", "gentle", "hardworking", "womanly", "feminine", "soft" and whatever, and then describe Western women as "aggressive", "angry", "demanding", well, what exactly are we supposed to think? In terms of women pursuing men the message is there, even if it's not overt: "don't".
I also think a lot of women end up with bad guys not just because bad guys pick up women and good guys don't, although there's a lot of truth to that (my husband is Mr. Amazing Good Guy but has always been terrible at pursuing women). It's also because those women are a.) fed the message that they're 'better' if they've caught a man (and we are fed that message, not always overtly but it's there); b.) happen to want love and companionship but aren't encouraged by society to pursue it, so they end up with some loser they know isn't good enough, because they don't know how to do it any other way; and majorly, c.) don't trust their intuition. In their gut they know a guy's no good, but they don't listen: especially if they've been totally conditioned to believe - consciously or not - that they are better with a man than they are single.
And it's not that Taiwanese men don't pursue women in their own way - they do. You could argue they are more reticent to pursue foreign women, and in many cases, especially among twentysomethings, this can be true. I'm in my early 30s and Taiwanese men who have indicated interest in me (not many, but a few) have all been in their 30s, an age when it seems to be much less of a problem (also, an age when Taiwanese guys stop being dorky kids in the night market and start being pretty cool guys). I can see how a twentysomething single female buxiban teacher or MTC student might feel she's not being pursued, because Taiwanese guys her age likely *are* more reticent, but an early thirtysomething might have more luck. I know it's said that 30 is the "cut off" for a woman's desireability in Asia, but I haven't found this to be all that true in Taiwan. I have plenty of thirtysomething single Taiwanese female friends and students who are happily dating or have good boyfriends.
It's that the "way" that they pursue women is not a way that Western women can easily pick up on unless they've been here awhile and have learned how to do it, and honestly, I can see why a single woman might not be all that interested in staying for 3-5 years just to learn how to read signals from local guys. In my experience that's how long it takes. I can understand why she'd get frustrated after a year or two and go home.
I can also see how a single foreign woman in Taiwan might not be able to cultivate the local social circle that I have: I do feel that being married gives me a sort of protective cover. I have local guy friends because their girlfriends aren't threatened by me (and my observation of much of the expat community is that while there are lots of local female friends and girlfriends about, having Taiwanese male friends - good male friends, no less - is fairly rare). I have local female friends who generally wouldn't hang out with foreigners: I have heard it said that in some circles, hanging out with foreigners, even if you're a local woman with a foreign female friend, is seen as 吃西餐 or "eating Western". Some (not all!) people will assume you're only doing it to get a foreign boyfriend through her social circle. My friends have not said this, but there's a good chance that, if I were single, I'd have fewer of them because they might, consciously or not, be afraid of being labeled that way. As a married woman I'm, I dunno, safer to hang out with. This isn't universally true but I think there's some truth to it. And when you don't have a local social circle, it's harder to meet local guys, who generally don't go trying to meet women randomly: they're far more likely to date classmates, same-industry peers or even coworkers, or friends of friends.
I know, I know. tl;dr...
But there's a lot to this topic and it can't - it simply can't - be boiled down to "Western women think Taiwanese men are girly because they're too picky or prejudiced". That's not really the issue, at least not with most (I've met a few for whom it is).