We have many different team members who do not use all of (or any of) our team inboxes, and do not need to see all of our message template folders mixed in with their personal message templates. It slows people down and is annoying to have to scroll through dozens of folders to see your own personal templates. We should be able to hide or remove access entirely from the folders so they don't populate when we open up templates in our private inboxes.
Indeed, you can't hide public templates on personal mailboxes.
You should have the option to hide a public template on personal mailbox.
And when selecting a template you should have the option to select personal or company templates.