I totally agree that at first it's confusing that Matrix the protocol has different clients, with unrelated names like Riot/FluffyChat/Nheko/Ditto etc. However, I really think this is unavoidable, just as it is with the Web, Email, IRC, XMPP, NNTP, whatever. And just as it would be incredibly arrogant and bad form and confusing for any of those projects to call themselves "Web browser" or "XMPP chat" or "Usenet" or "Mail client", the same is true for Matrix. Yes, it's more cognitive load than a system like Slack or Discord where there's one official client which bears the same name as the service, but it's a fundamentally different beast.
In terms of Matrix IDs, we very very deliberately made up the @user:example.com format to avoid folks ever confusing them with email addresses like user@example.com (and to hint at a federated form of @mention notation, a bit like ActivityPub subsequently did). We find it super confusing that SIP URIs and JIDs look like user@example.com if you drop the scheme prefix (as often happens), given there's zero reason why user@example.com on email should be configured to correctly route to the same entity as sip:user@example.com or xmpp:user@example.com - and in fact the chance of it working in the general case are incredibly low (thanks to aliases, filters, routing rules, etc).
That said, we do not expect Matrix IDs to be used in the general case - we've always wanted people to discover each other based on their existing identifiers (email, phone number, etc). In practice this hasn't gone smoothly as nobody has properly solved decentralised identity (or if they have, they haven't hooked it up to Matrix yet), so we're in a bit of a limbo. But the solution is definitely not to make Matrix IDs look like email addresses.
So, my point here is that this is not "technically correct is the best kind of correct". If we renamed Riot to be "Matrix Client" we'd be quite rightly crucified by every other Matrix client developer out there. Just like Mozilla would if they renamed Firefox to be "Web browser" (even though they were effectively responsible for the modern web browser as Netscape).
However, we absolutely have made things even more unnecessarily complicated by maintaining separate brands for Riot, Modular and New Vector, hence consolidating them together. But we simply can't get away from the fact that the end result will be a Matrix client, not the Matrix client.