As shocking as it may seem, you probably are flowing slightly more air for a given throttle position. Therefore burning the extra fuel. Probably doesn't account for all the loss of economy though, as 10% is a fair bit.
Running without a heat shield is probably not the best idea. It's unlikely to make anything go pop, but nice chilly air is the ticket

There is one sure fire way to find out, stick a proper filter back on it and see what happens.