Maybe this exact question has been endlessly discussed on the Helpline, but so far the answers to Emily's post have been very one-sided.
I choose to fly Lufthansa because they go where I want to go, and their service is a world better than US airlines. And I carry-on because I know if I don't, it's just a matter of time before I arrive without my checked luggage (it's almost happened three times). Lufthansa has an 8kg (17.6#) carryon limit. Other quality airlines have similar limits. SwissAir is also 8kg; SAS and AF may allow more. Alitalia and Aer Lingus are out of the question with 13#.
With a 2# convertible bag I can live with the Lufthansa limit, but with a 7+# rollaboard, I would be limited to about 10# of "stuff". If that's all I'm allowed, I don't need wheels. I can put it in a 1# duffle and carry it easily.
The advantage to wheels is you don't have to carry it; the disadvantage is it's so heavy you can't carry it - and sometimes you have no choice.