You already have the standard operations anyway. They're called "functions" and "operators" and such. And you do need a common representation for that between client and server.
Right now, that common representation is text and SQL, plus (sometimes) a server-specific method to prepare statements to prevent having to transcode and quote data.
Replace that with XML or whatever all you want. Doesn't buy you anything. You still have to assemble a textual string on one end and analyze it on the other side.
Three choices here:
* stay with SQL. It mostly works, people are used to it, you can do interesting stuff with it in any programming language whatsoever. Downside: you still need server-specific code for more complicated queries and for schema.
* agree on a common high-level API for queries, and possibly for schema queries/changes. Downside: who'd do the work and who'd agree on the result? The commercial vendors? Hardly.
* agree on a common binary data stream between client and server. Same downside, plus doesn't work for embedded servers.