is the man or bear thing rhetorically or optically the perfect feminist meme that is beyond criticism? no.
but is it leaps and bounds better at getting men to understand the material consequences of patriarchy on the physical and emotional health of women than that stupid “kill all men” meme from last decade? definitely.
Combine this with the expectation that one sex is expected to do nearly all such soliciting.
I actually find it amusing that Bumble recently announced that they are no longer going to require women to make the first move because many find having to do so a burden. It’s something of an intractable problem - women don’t want the burden of having to do the approaching and potentially facing rejection but also don’t want to be approached by men they aren’t interested in (and tend to have much lower tolerances regarding the behavior of said men - a lot of behaviors that are “flirting” when done by a man they’re interested in are seen as something else entirely when done by the wrong man).
Then from the other direction you have men for who it’s largely a numbers game - many men don’t put much effort into the messages they send out on online dating services because the response rate is so low. If a large majority of your messages get no reply, it’s less psychologically painful to think about the sheer number of times you’ve been considered not worth the effort to bother turning down if you aren’t investing as much into each attempt, and if you aren’t investing much into each attempt then you can make a lot more attempts for the same time investment. Response rates are low enough and the difference in odds of success between low effort and high effort messages small enough that it impacts the entire thing pretty heavily.