Ironically spacex is most likely to provide a budget friendly route to space on an industrial scale - and is already cutting costs by a significant amount. Only reason they used the Ariene 5 was because of its width.
Not even that - the Falcon 9/Heavy fairing is the same width on the inside as Ariane 5, only the exterior is narrower (but the walls are thinner). The rocket simply didn't exist at the time when JWST was designed, and changing the launcher for a project of this complexity years after the design and build started wasn't even considered, understandably. But it will be very different for future projects.
Yes, as I understand the Ariane 5 was the widest reliable launch vehicle available at the time. Obviously trying to fold the telescope into a smaller space would have introduced even more complexity so they chose it - changing later would have added delays and additional complexity!
It has nothing to do with reliability or space. Its political. ESA put in the budget for the launch and they got a significant part of the science in return. And ESA of course put it on Ariane 5. There was no competition or comparison or any of that.
Since then the price of the rocket has gone from like 20%+ to like 2% or less of the cost. But they will still get the science. So all in all, might be the best investment anybody has ever made in terms of a science project.
The Delta 4, Delta 4H and Atlas 5 would all have been fully qualified to fly the JW and likely could all have launched it. Maybe the Atlas 5 is to small but there were certainty rocket in the US that had the required certification from NASA.
edit:
its payload width*