And that is key. Indeed, competitive pressure drives evolution (but isn't the strictly sole driver or the mechanism of evolution itself). The most important point is: evolution only values survival/reproduction, it doesn't value "progress".
There's a very strong argument that humans now understand evolution enough to make conscious decisions not to just play the natural competitive game. We can actually make a better world by refusing to follow that natural game. Life in competitive natural circumstances is brutal, painful, and short. We value progress as in human (and non-human even) flourishing, happiness, scientific progress, etc. and we get those things best by refusing to just act like competitive evolution but instead by rising above that. For example. we have no evolutionary benefit in caring for the least among us as an entire global human society but when we do so, it's because we recognize the ethical value.
>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.
actually competitive pressure is the primary driver of evolution. Some aspects of evolution when applied to humans we call progress.
>There are tons of cases where reduced competition and increased cooperation can provide more progress.
cooperative behavior in a group evolves when it helps the group to compete, and thus it may result in increased competition between the groups. Organized human society would be an obvious example of cooperative behavior. Massive battles and wars and other atrocities inflicted by the human societies upon each other, and overall effect of the human society upon the rest of the Earth species doesn't seem to qualify as reduced competition. If anything, increased competition between organized human societies, like wars for example, has significantly sped up the tech progress as a result of the need for weapons development.