Thanks to everyone for their replies. As the original questioner, I've deliberately come late to this party.
I think it's instructive (and fun) to look at GM Kramnik's arguments from the perspective of the collectable card game Magic the Gathering. Think what you may about Magic, its developers are the absolute experts in rule changes, since they've been doing it continually since 1993. How might an imaginary Magic Developer respond to Kramnik's (paraphrased) arguments?
Kramnik: (1) There are two related problems: too many draws and opening theory carries on too long into the game.
Imaginary Magic developer: "YES absolutely. We try in Magic to avoid draws and drawish positions, which are anathema to player fun. The too lengthy opening theory in chess shows clearly that the format is too nearly "solved" and needs refreshing. You poor guys!"
Kramnik: (2) Chess960 won't interest spectators, won't interest some players, and is not "aesthetic".
Imaginary Magic developer: "NO WAY. Fischer's genius invention of Chess960 is the nearest that chess has to the concept of "printing new Magic cards". It's a great way to expand the game and make it fresh for players and spectators. The recent World Championships in this format was a resounding success, with commentators on the edge of their seats right from the beginning of the game. It must be very difficult for professional chess players, who have invested their lives and bet their economic future on a particular form, to contemplate their main asset being devalued by Chess960, when there are always newcomers and computers to adapt to the new formats quicker. This is really hard, but I don't think you can use this point anecdotally to argue against Chess960. And I think you confuse "aesthetic" with "familiar".
"We Magic developers are sensitive to the views of the pro player community, because we understand that where they lead the rest of the community can follow. But we can't let a key format decay indefinitely."
Kramnik: (3) Chess would benefit at top levels from banning castling .
Imaginary Magic developer: "This is a very interesting proposal. We are alert to the playability of formats, and will sometimes step in to ban powerful cards if the format is not healthy. We particularly focus on the balance between attack and defence, and here arguably the classic chess format is suffering, due the capability of computers and players to find better defences against (sacrificial) attacks. Castling is a powerful card, a kind of "Black Lotus", offering "three tempi for one". Castling also resembles the pattern of recent conditional Magic cards, in that there are some preconditions that you need to satisfy, but those are the kind of things that you would want to do anyway (develop minor pieces, avoid checks). So the preconditions aren't really a downside. Only a player of Carlsen's calibre has been able to reliably eke wins out of drawish positions: which is what needs to be done if romantic-style attacks cannot be successful. So here we do need to shift the balance from control to aggro."
"Removing castling at the top levels of chess is an elegant proposal, and may help fix draws. But we don't want to separate the game the Pros play from the game that our paying public plays. And banning one kind of move can only refresh chess opening theory as a short-term side effect. Ultimately chess need to "print new cards" with Chess960. This is the real future of chess."
"Castling by the way sits uncomfortably in Chess960 anyway (even top GMs don't know how touch move works with it) and is arguably unnecessary. We Magic developers are alert to fussy rules and would try to get rid of castling in Chess960. Since Chess960 is new, we don't lose any history by so doing."