There's folk Oop North bitter enough about the cost of a two track Crossrail - they'd have a coronary if you doubled the costs to design a four track Crossrail! Much better to use the "spare" money for Crossrail Two on a different alignment (Wimbledon to Islington).
With the train operation being automated, and Crossrail originally designed to have only having a couple of "shortish" branches at either end* (i.e. much less complicated than Thameslink is going to be, much shorter than Thameslink is going to be), trains should cope with the central "core" without much fuss.
Crossrail is going to be a simple route, like a grander version of the Central Line, rather than the four track/ freight/ Bristol to Norwich express/ double decker (delete as applicable) line that some enthusiasts want it to be - the reality of Crossrail is probably going to seem quite boring once it opens (efficient, simple, roughly on budget, roughly on time, no doubt well used from day one... but not as "sexy" as the Enthusiast Community would like!).
(* - pre "Tring")
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Although I totally agree with the gist of your argument, I can't see that 4 tracks would cost twice as much as 2 track, especially on the station side
FOUR tracks could cost more than double TWO tracks, since a two track railway only has to find a "gap" of a certain width between various underground lines/ rivers/ other tunnels under London - finding a route for a wider railway may be significantly harder.
(I don't know for certain, of course, just explaining that sometimes there are economies of scale and sometimes there aren't)