Some of this is fair criticism of Oxbridge, some not so much.
The 'grand formal settings' for interviews are the buildings most of the colleges have -- and one of things that make them such incredible places to live and work. Yes, you could erect a small, casual prefab to conduct your interviews, but that would be kind of dishonest.
On the other hand, Oxbridge probably is unhealthily attached to some of its weird old traditions (gowns, Latin, port, etc.). These things also vary widely between the colleges -- but in ways that are hard to find out unless you are (or you know someone who is) on the inside.
I went to Trinity College from an inner-city, state school background and always oddly enjoyed the weird traditions I experienced when studying there. These experiences coupled to the history and the grand buildings always made it feel as though I were studying in a museum which, in turn, really fed my imagination/curiosity to explore what else was out there (in terms of odd rituals/behaviour e.g. announcing exam results on the steps on Senate House). I doubt that was their intention but it was an interesting side effect.
What's unhealthy/weird about it? I've been at several Universities and each of them has their own 'traditions'. Also, I wouldn't really call the examples you gave as 'oxbridge traditions' (you're right that things vary a lot by college).
One wonders what she'll make of the place she wants to go (UCL) where they keep the body of the founder on display in a glass case in the main hall, and he's wheeled into meetings and listed in the minutes as "present but not voting"?
Not to mention that UCL is just as "elitist" as Oxbridge, and aspires to be more so...
* "If the Proctors consider you not to be dressed correctly they reserve the right to refuse you entry. Any infringements involve the Praelector in paying a fine of a bottle of Port!" (http://www.clare.cam.ac.uk/Graduation-2011/)
-- which serve no obvious purpose, but can potentially make people feel that Oxbridge students are strange and different (and maybe posh or snobbish), and not the kind of people they'd like to be around or become.
I'm not saying this is always an easy call, though. Once you're there, a bit of harmless tradition can of course be fun.
I can see your point but academic dress is used at many institutions. The only difference here seems to be there are more occasions in Oxbridge where people are required to wear it.
You also say ...but can potentially make people feel that Oxbridge students are strange and different..., which I completely understand. However, I get the impression that Oxbridge gets a lot of attention and people almost look for the idiosyncrasies so they can point them out. I've never heard of anyone being fined bottles of port at Cambridge but I wouldn't be surprised if there were such rule written down somewhere in the last 800 years. It's akin to strange rules like commoners not being allowed to drive sheep through London. It might still be illegal but no-one pays it any attention (nor can they be bothered to repeal it).[1]
(Disclaimer: Grad school at Cambridge)
[1] I have no idea if that's true and I've heard variations that involve tolls and geese. My point is that although such outdated laws exist, no-one really goes looking for them.
A dress code is a dress code. If you go in short, no shirt and flip-flops to a club they wont let you in. Why will the most historic/renowned/respected university in the world does not have the right to impose 'admission criteria', in this case clothing.
The 'grand formal settings' for interviews are the buildings most of the colleges have -- and one of things that make them such incredible places to live and work. Yes, you could erect a small, casual prefab to conduct your interviews, but that would be kind of dishonest.
On the other hand, Oxbridge probably is unhealthily attached to some of its weird old traditions (gowns, Latin, port, etc.). These things also vary widely between the colleges -- but in ways that are hard to find out unless you are (or you know someone who is) on the inside.