Do you think there are many interesting niches left for new supports to occupy? Bard is fresh, but some of the old-ish true supports already have quite a lot of overlap (Nami, Sona & Lulu, for instance).

Yeah, you're onto something here.
When we were much younger, we just struggled to make a champion, any champion, every other week. This was seen as crucial to our survival as a young, small game. Eventually we realized this wasn't great for the game as a whole; non-differentiated champions are mutually cannibalistic. In simpler terms, say champions A, B, and C all do the same thing (let's say "put down damage at great distance", and call them Lux, Xerath, and Ziggs), inevitably one of them will be seen as being the best at that role and the other two will stop being picked at all in competitive environments such as ranked.
(This was actually a bad example; Lux is a catcher in our internal parlance, while Xerath and Ziggs are artillery. Ziggs is differentiated from Xerath in that he's the better zone controller and in that he has better side lane pressure. Xerath is the sniper you bring when the enemy has an immobile squishie backline with tons of damage.)
This is why we have Roster team! Their first major project was the Juggernaut update. Previously, most Juggernauts did the exact same thing in that they ran at you and crushed you if they got to you, but were easy to kite. Whatever else you may think of the Juggernaut update, the four champions we touched now have VERY different identities.
Roster team is now working on the marksman class (what a tough one that will be! How do you meaningfully differentiate champions whose main output is right-clicking your face?) (they have some very cool ideas, but it's too early to talk about it). You identified a subclass of support we call the enchanter, and yes: enchanters are also very much in need of some roster team love. I'm sure they're on their backlog.

The answer hasn’t got any rewards yet.