There's also some assumption here that civilisations either collpase or conquer the galaxy, but that ignores another possibility - that civilisations might quickly reach a plateau technologically and in terms of size.

The reasons this could be the case is that civilisations must always solve their problems of growth and sustainability long before they have the technology to move beyond their home planet, and once they have done so, there ceases to be any imperative toward off-world expansion, and without ever increasing economies of scale, technological developments taper off.