Amazon's Send to Kindle address is an email address. Attach the EPUB and put "convert" in the subject line. The file lands on every device on your account, and Amazon converts the format for older devices that do not accept EPUB directly. That is the whole workflow, and it works from a phone.
These read EPUB natively. Kobo also has its own KEPUB variant, which is an EPUB with a little extra, and some Kobo apps are pickier about it. USB is the reliable path: connect the reader as a mass storage device and copy the file into the books folder. On a Boox or a PocketBook you can also install KOReader, which reads EPUB, PDF, DOCX and CBZ in one app and renders PDFs with reflow.
Apple Books takes EPUB and PDF. On iOS the file comes in through Files or a share sheet, and it is usually easier to convert first and open the EPUB than to read a PDF in a viewer that cannot reflow.
MTP file transfer has been getting restricted on newer firmware. Copying over USB still works, and Send to Kindle by email is unaffected, which is why the email route is the one that has not broken for anyone.