You can't post anything in the language partner section but you can only search profiles. People post here because the language partner section doesn't work and is almost impossible to find in the app. It's very well hidden.

The same menu, "Community," that contains "Notebook," "Answers," and "Discussions," also contains a section called "Language Partners."

That's where you're supposed to look for language partners.

I don't know why people post in "Discussions" instead, and or why, lately, there's been such a huge increase in people doing this.

You are right. If we think about it, it is the only way members can show to the comunity that they are avaliable and interested in practice. I use to post in the discussion section, but my level isn't good enought to express my ideas, so it is not so frequently.

It isn't a big deal. You don't have to click on the links going to their request. It isn't that hard to scroll down and go to a the next discussion page. The trend of "hating on language partner posts in the discussions" is counter productive to what this site was initially meant for. 

Besides if you  want to you can turn the requests into a discussion if you are feeling ambitious.