Actually, whether to use wire or not depends a lot on the rabbit. A study showed that most rabbits actually prefer wire, as long as they do not only have wire and do not have already sore feet or poor furring on their feet (which is what leads to the sore feet in the first place). They put rabbits in cages that were half wire and half solid bottom. They put a food dish and a water bottle on each side of the cage, so rabbits would not have to move onto or off of the wire if they did not want to. During the study, they found that most of the rabbits prefered to stay on the wire side, with only a small percentage prefering the solid side. Both sides were kept very clean, so dirtiness was not a factor in the rabbits choosing one side over the other. Not only were the rabbits witnessed spending more time on the wire side, but the food and water containers on the wire side emptied much faster than on the solid side, showing that the rabbits were on the wire side eating and drinking more than on the solid side.
Certain breeds, like rex, mini rex (looks like you have a mini rex, from the picture), and giant breeds (flemish giant, checkered giant, etc...due to their weight) sometimes are prone to sore hocks (the sore feet) from the wire, and some do better on solid flooring than on wire. Another alternative (and my first choice) is to line at least half of the cage with plastic resting mats that have holes for the urine and feces to escape, but provide much more support than the wire alone does. These are much more sanitary than solid flooring. With solid flooring, if a rabbit has parasites, it can keep being reinfested by the eggs and the adult parasites. Wire cages (and the plastic resting mats) are much easier to keep sanitized and don't hold bacteria like wood, shavings, and other litter does. It also keeps rabbits from digging dirty litter and feces into their food and water containers (which is very common among rabbits, the little brats lol).
So really, as long as the rabbit is not subjected to just plain wire with no relief, wire is actually a good choice. It just needs some touches of comfort, like a litterbox, resting mats, and a nice area to sleep on (preferably NOT made out of cloth because rabbits can tear cloth up, eat it, and get serious intestinal blockage which can be life-threatening...metal or hard plastic nesting boxes with fresh straw make for good, easy-to-clean beds as well as for giving birth, and as long as it is not placed right next to or over where the rabbit goes to the bathroom, they generally don't urinate or deficate in the box much).
Just in case you were not aware, you rabbit looks like a broken castor (the colour) mini rex (the breed). My favourite breed! He's a cutie!