No, aircraft land on carriers while applying full forward thrust and (I am 99% sure) no wheel brakes. The idea is that if the wire fails to catch they "bolter", i.e., do a touch-and-go, so they can come around for another landing attempt. (If they stopped or reversed thrust and the wire didn't catch, they'd end up in the drink.)
Based on other comments (or re-reading the authors comment carefully), it turns out that "wire only" mean that the wire catches before the wheels touch the ground. (This puts additional strain on the wire and airframe.)
You're correct, no wheel brakes and throttle to full as soon as the wheels touch.
If the cross-deck pendant snaps, the engines don't have time to throttle up before you go over the edge. And of course if you don't catch a wire you really don't want to be trying to stop.
There are brakes on the wheels (that can slow a plane moving at flying speed)? That's a lot of force. I assumed the wheels merely prevent friction between the plane body and the deck, and the engines and control surfaces, and the wire, did the braking.
"no wheel brakes" here means that the brakes aren't engaged, as stated so that if the aircraft misses the wires it can touch and go without drowning the pilot and destroying an $80m aircraft
Based on other comments (or re-reading the authors comment carefully), it turns out that "wire only" mean that the wire catches before the wheels touch the ground. (This puts additional strain on the wire and airframe.)