"The next steps will be to join both halves of Webb to form the fully assembled observatory and complete a final round of deployments, testing and evaluation prior to launch,"
So it's still not ready to launch, and there are potentially many more opportunities for issues to crop up pushing it's budget even higher then its already astronomical 10 Billion dollar price tag. Don't get me wrong, I think NASAs budget should be doubled and a lot of the strings that Congress attaches to various projects (build the engine in my district, open a research center in mine, etc or no money) should be cut, but the procurement process needs a complete overhaul. The cost plus contracts need to be ended and contractors shouldn't get a dime until they achieve verifiable project milestones. If they fail at any stage of a contract all of the hardware, software and documentation developed up to that point is turned over to NASA to rebid the contract without losing the previous work. It's to be expected that projects will run over-budget once in a while, but lately every major NASA project has doubled (or more) it's initial budget (Constellation, SLS, JWST, etc).
The overhaul for certain, but there's a few major points that are ignored or contradictory in your statements.
With initial budget under-bid and undercut, it is automatically going to cause over-budgets when reality sets in. Also, what is criticized as "over-budget" today is often simply reaffirmation that originally approved budgets were truly undercut (and originally estimates were indeed more accurate than the over-estimations claims the critics throw around at the time).
The various aspects to a project funds reflect scientific hypotheses on time, materials, operating expenses, and other budgetary needs... including anticipated technology transferring from laboratory settings to real-world development (although not "commercialization" in the economic sense). What this means is that certain scientists become available/unavailable, raw material procurement is challenging (i.e. rare earth elements, import tariffs), facility operations may become hampered (esp. when natural disasters affect the areas), and progress in computer modeling is negatively impacted by regular challenges (i.e. computer malfunctions, delayed provisioning of systems, etc).
The hardware (i.e. measurement equipment), the software, and the documentation (which should reflect the systems as-built and not as-originally-imagined-5-yrs-ago)... are not necessarily transferable to new bidders or new development teams. Sometimes the science behind the custom-built equipment is wrong (so there's a sunk cost in its failed component development), sometimes the math is wrong (thus impacting the overall science), sometimes the roadmap changes (so the equipment is expendable due to increased efficiencies with other equipment already within project scope, "primary/secondary" functionality)... and thus the software and documentation follow the same path (directly as a consequence, or indirectly due to similar reasons). To believe all work is immediately transferable is ideal but realistically naive.
Overall, this JWST project seems to have had more unified support than many other projects within NASA (ahem, at the expense of the other projects at NASA). But just imagine, for a few seconds, what wild and ambitious work NASA could be doing if it had more government support across all branches, and the inflation-adjusted budgets from past generations!!! But you're absolutely right, there's so much potential for NASA lost to government politics that multiplying their budgets would not result in multiplied program successes... and that's the sad truth.