We take ours to the vet in one of those sturdy plastic carriers when we go, too.
While it would be nice to let one or the other sit on the car seat beside us (or under the seat, as has happened), it's easier to drive and have a cat in a carrier than it is to have a cat wandering around on the pedals when I'm driving. Sometimes, they are a bit lacking in common sense!

As has already been mentioned, it seems better for our cats to be in the carrier once they get to the vet...partly because of the "new environment" they're going in to (new sounds and smells) and for the aspect of who and what's been on the floors.
When we have appointments lined up for our pets at the vet, we bring the carrier inside the house first to let the cat that's going to the vet that time get used to it. And, because I live in a cold country, a carrier that's been on the porch in 10-15 below zero weather would not been too inviting to kitty paws or tummy.
We do have to make sure, though, that when we're ready to go to the vet that we've got the right cat in the carrier. Because once that carrier comes in the house, we seem to have a free-for-all and they all like to get in it to see what's going on.
In response to your question regarding whether it's large enough; the carrier you picture seems like it might be a bit small for a 20 pound cat.
Another thing to consider when taking a cat to the vet (or elsewhere), is the small space like that could give the cat some sense of security.
Karen