Eaves are often a preference because most people choosing them don't even understand the function of them. Plenty of modern and architectural designs do not have eaves full stop. And the builders charge well for the work they do, so cheaper doesn't even come in to it.
Sure the op should have his issue resolved (compensation or not), but there is no doubt his claim of it lowering market value is rubbish. That's the point.
If you don't get that, I can't help you.
GLHF