I've never heard of wearing bags crossbody being "tired", and the practicality can't be beat. I have both hands free, I can get things out of my bag with one hand if necessary, and it doesn't slip off if I need to look into it. I wish all bags had an adjustable strap option.
Considering how expensive some bags can be, I can't help to think how easy it would be for someone to snatch it off the shoulder. The few times I'm in a rush, my bag will go briefly on the shoulder, but the second I have a moment, I switch to crossbody. I have never owned, and don't see my self getting, a top handle bag.
Keep in mind that I get around a big city using public transport, so that heavily influences how I wear a bag. For me, function will always come ahead of form.