We still support our pre-Transifex method of translations, which is to edit the files locally in something like Poedit. We accept such edits as either Git pull requests or simply emailing the file. So I wouldn't say that we "depend" on Transifex, but instead we use Transifex to supplement our existing translation methods.

I hadn't heard about Weblate, but the interface seems nicer than Transifex in some areas. However, I chose Transifex since it was requested specifically by some of our translators. The popularity of Transifex itself helps our goal of trying to expand our pool of translators. We'd miss out on that using something smaller like weblate.org or self-hosted.

I think the freedom-conscious translators will just have to stick with offline/desktop translating for now. Github uses non-free JS, too. But people still can use email to report issues and send patches. The same applies for translations.