From the point of view of the website, you're not driving clicks. You're not making money. You're not driving growth.
It is also bad for users. You do not drive clicks. Cannot pay for marketing. So your site gains no traction. And with no traction, actual users show up, can't find the people that they know, and then leave the virtual ghost town.
Therefore it sounds logical, but fails in practice.
Now add in a single feature. Add notifications to people saying that X people like them. Now people have a reason to come back. A reason to click on others. You get growth. Your website can make money. And you've become a spam site which completely lost the original idea. But you're a profitable spam site. And will probably drive more actual hookups than the pure form.
And this is why dating sites either fail trivially, or go on to suck.