I keep haring that this is a myth:

However, in the real world, a tyre that deforms to rough surfaces is more efficient than one that bounces on top of them.

And yet, the way I can tell I need to inflate my tyres is that I feel really unfit. And as soon as I do inflate them, cycling suddenly becomes easy.

The larger tyres that I've seen are much more rigid than an underinflated small tyre.