The cost of Ariane 5 rocket is below $200m, which is a rather small fraction of the overall budget of $5-10b. If the main reason for the huge cost is to make it so lightweight, why didn't they go with more capable heavy-lift rockets to cut some R&D costs already? At least, Delta IV Heavy seems to have a significantly larger max. payload [1]. The JWST was still in re-planning phase as of 2005 and Delta IV Heavy was already operational at that point.
[1] https://en.wikipedia.org/wiki/Heavy-lift_launch_vehicle