Can you confirm that you have previously purchased FCP?
Although you mention "Purchased" section, it is not overly clear, to me at least, that you have actually purchased FCP previously.
I say this as some people believe that the "Purchased " section is where ,on the App Store, FCP is offered for sale, rather than the page that lists the applications that have previously been downloaded for free or paid for.
If you have indeed never purchased FCP then the method you outline never has offered you a compatible version for your opperating system, even though you are quite willing to pay for it.
If you have actually purchased FCP before now ,then, as Luis says, it seems not possible to re-download an older version ,even if it is the same older version that you previously downloaded.This might be the situation if you had to replace your HD or SSD and wanted to re-download your applications.It does not seem clear how far back you can or cannot go to download an older version onto what operating system, that until recently you were able to do.
When I saw on this forum ,about a month ago or so now, that someone could not re-download FCP from their purchased page, Luis may remember this as he was able to confirm this by trying it, I thought I would experiment to see if I could re-download iMovie on an old El Capitan set up, having made sure that the current version was put in the trash. I was indeed offered the compatible version for El Capitan.Whether or not Apple are treating free apps differently to paid for apps, who knows?
Subsequent to this, another post in iMovie shows problems in re-downloading iMovie for an older system because the hard drive had failed.The OP had problems achieving this but after several attempts over several days he got there.So are free apps OK but paid for apps not?
Quite bizarre if it is the case that you cannot re-download FCP from the purchased page for older operating systems and how far back those operating systems are affected, older than the 3 most recent for example?
Surprising that there has not been more about this on this forum. Would you pay £$300 for FCP if you knew you could not re-download it if you had to?