Stupid POP3 accounts. This is often the result of adding a POP3 account to a new device, or deleting and re-adding it to a device.. It, the server, has no way of knowing what emails left on the server are new, so it gives them all to you again.
Anyway, if your provider has a webmail site, try selecting and deleting old emails there. Even the trash, if you are certain you don't need anything that is in it.
And if they offer an IMAP or Exchange server, switch.
That's not to excuse Apple from the lack of a select all/delete option. It's rarely needed for the Inbox, but when it is needed it's usually a desperate need.
The Trash and Junk folder do have a select/delete all feature.