Downloading from Google drive doesn't cost anything, does it? Although, I guess you would have to have enough empty space on your Google drive to be able to store the takeout zip, which I think is an acceptable cost
Androids implementation doesn't even have an extra step of screenshotting like iOS. You can just swipe up to open recents screen and start selecting text by holding down. Although it's not as good as native selection since it does some kind of OCR vs actually selecting the text data, so it cannot properly copy things it doesn't understand like random languages or hashes/urls etc. It does has it's own advantages though since it can select anything like text from paused videos vs only rendered text views if app allowed native selection).