I've never used Matrix and I'd love a replacement for Slack/Discord. But hearing "I generally steer them towards the Element clients" is going to be a huge turnoff for a lot of non-tech people. Even as a tech user, I don't really want to compare and research different clients to figure out which is best.
The difference is in marketing. Gmail is a service with its own official app and so on. Matrix is a protcol, you can't market a protocol to regular people. Other than techies, nobody cares how their chat works as long it works so if you want to gain traction you market Element as the new hot messaging app and not Matrix the protocol.
I don't think that's a good example since Gmail is an email provider which can be used with any email client. Element is a Matrix client that can connect to a matrix provider.
What do you propose to do instead? To actively prevent people from creating clients for the protocol?
The Element clients are the closest to what you could consider official clients, being made by the Element company, which does most of the Matrix design and development.