Isn't this what Google is essentially trying to achieve? Email, video streaming, advertising, etc...
Reply to sibling: Why would anyone call an email provider a walled garden, especially if using your own domain name?!
I know FastMail is working on JMAP, which ideally will be a new standard that supports labels, but if it takes off, it'll be a number of years before labels is something you can assume a given mail client will support. I use platforms that rarely have official app support (aka, not iOS or Android), so wide standards compliance is a big key.