The regulator forces banks to assess their (intraday) liquidity risk in normal and stressed conditions see e.g. BCBS 144 principle 9. To me this sounds pretty much like a possible application of EVT to banking - not (!) asset - liquidity.
However, I find it hard to find referenes of an application of EVT to the liquidity of banks -especially something up-to-date. Can we collect some here?
EDIT: I found this thesis: Intraday liquidity risk estimation using transaction data: an extreme value theory approach. If I interpret the conclusions correctly then the result is rather mixed.