SFTP came along as basically a working, feature-complete replacement. Once it became production-ready, I don't think there was anywhere for FTP to go.
Or HTTPS, IMO; it supports file download/upload, user/pass access control, and encryption. It's a little annoying to have HTTP subsume yet another thing, but it's actually pretty decent at this one.
The FTP standard has a number of features that SFTP doesn't include, such as record-oriented file transfer (STRU R, MODE B), store-unique (STOU – you upload the file, the server picks the name instead of the client). Many of these features are rarely used, and many clients/servers don't even implement them, but SFTP is not a feature-complete replacement for FTP. But there are some environments (e.g. mainframe environments) where these features are used, and these feature gaps make it difficult or impossible to replace FTP with SFTP
FTPS is still used in mainframe and minicomputer systems as well. This is because FTP has native support for transferring record-oriented files – STRU R and MODE B/C. Those features are generally not implemented by FTP clients or servers on Linux/macOS/Unix/Windows/etc. Unlike FTP, SFTP does not have native support for record-oriented file transfer.
I understand that GridFTP is still used in high-performance computing applications. GridFTP extends FTP with features such as parallel data transfers targeted at transferring massive data sets (terabytes, even petabytes in size) over very high bandwidth links. (Aspera performs better but is proprietary; GridFTP is an open standard with open source implementations.)
In the case of NCBI, the actual transfer protocol usually used is Aspera, but you use the FTP server to find what files you are going to download using Aspera (which is CLI only AFAIK). Thus in this workflow, browser support for FTP is actually important.
I would say that the reason it hasn't changed is that it does its job fine. It serves files. It's one of the simplest ways to do so, and I lament that in my sphere the biggest apparent replacement is Dropbox. I agree with one comment above that "legacy" code for FAANG is apparently "features which we can't monetize".
Meanwhile the biggest problem with FTPS is just that people misconfigure their own firewalls to prohibit outgoing connections to arbitrary ports for no good reason. (Spoiler alert: All the bad outgoing stuff these days is on TCP/443). Which fails by getting your users to complain to you to fix it, instead of failing by silently giving attackers instant RCE.
I think FTP is being kept-alive only by legacy fintech (doesn’t the US ACH depend on banks exchanging CSV or TSV files over FTP?) and low-end shared webhosting services that are too afraid to offer SSH to their customers.
But I don’t understand why FTP didn’t receive much love from the IETF+etc in the early 2000s to keep it relevant. I know many saw WebDAV as the future, but that was too idealistic imo. Why didn’t any of the FTP server vendors get-together to fix their collective shit instead of letting it die? (No, PASV-mode doesn’t count).