tomcat et al,
the towbarless (tbl) wraps itself around the wheels, it can be done when the ac is parked and it dosn't lift the ac before push.
Paxboy,
yes it saves money. Many stations are allowed to do a one man tbl operation. Furthermore, there is one less link to turn so it is easier for the driver than with a towbar, resulting in less aircraft damages - the most usual being nosewheel limit not kept.
I really wish I knew a lot less about ground handling....
/fs