Good point.
Next time I have either Tyre changed, I'm going to ask the Guys at the shop to throw the wheel on the balancer before they remove the old Tyre just to see what it's like.
This could be one reason why a new Tyre always "feels" so good, that is apart from the fact that we now have a "proper" profile Tyre.
Rear Tyre's I don't find too much different as I wear them the full width of the tread, so they still have a "round" profile.
But front tyres, I cut the sides off with still plenty of rubber in the middle, so the profile of the Tyre is way out of shape.
Having said the above about the rear Tyre, I still notice a big difference when I've had a new one fitted.
Especially so if I've done both tyres at the same time, the bike is quite different.