On requests that change the cart content, I want regular dynamic page calls, so I don't think it'd be too much of a problem getting the cookie updated server side. A whole heap of stuff needs to checked anyway, like how many items are still in stock, and whether the resulting cart content would be available.
But when the cart content is not changing I want a cached page with a number stored in a cookie displayed on the page. It would probably be very easy to use javascript to print the contents of a cookie into a page, right? That's even an acceptable solution... people without javascript could always just login to get their cart contents displayed properly, it's more of minority issue.
But why wouldn't having a single line like
<?php
print $_COOKIE['cart_counter'];
?> in the cached page not work with boost?
What about regular page caching?
Making unnecessary ajax requests slows your site down, that's my main issue.