Except when it doesn't. It's perfectly possible to have, for example, a bunch of scientists crazy motivated to learn the answers to their questions and all collaborate as cooperatively as possible toward that end. Adding competition could result in duplicated effort, secrecy… or to added pressure and motivation… I mean the one thing we can say is that there's no guarantee that competition is good or bad for progress, it depends on so many factors.
You can reasonably say that competition can drive progress. Your sentence implies that it is the primary (or sole??) driver of progress, and that's nonsense.
Consider Richard Dawkins' tree analogy: competition is what drives trees to become super tall, but that means they spend tons of energy doing that. Being tall in itself has no value to the trees. Yes, evolution inherently creates ecosystems around tall trees, but that doesn't mean that particular ecosystem is somehow better than other possibilities. It's more true that competition is just a fact of life rather than that we know it to be good or bad. There are tons of cases where reduced competition and increased cooperation can provide more progress.