The only advantage I see to "heats up quickly/cools down quickly" is actually more a function of the cordless aspect.
The dog can't trip over the cord, and turn it into a BRANDING iron.
Not that that has ever happened at MY place, or anything.
(Actually it BARELY missed him, and hit the carpet).
It's not the soldering iron that needs to be hot to solder anyway, it's the connection.
Regardless of how hot the tip is when it makes contact, it still has to remain there long enough to get the connection hot.
Starting with the tip hot seems like a plus to me, if anything, because it doesn't have to sit there as long that way.