Throwing some rough and ready math at the question, happy to be corrected by anybody with actual numbers.
Hardening increases the radiation level to trigger errors by several orders of magnitude, call it 1000 for this.
Dropping the radiation by a factor of 1000 to a 10cm cube would take about half a mm of lead, adding up to something like 250g. Most computer modules are larger and more awkwardly shaped than that so couple of kg of shielding.
So shielding would be achievable but would cost an instrument or backup element out of the final design.
What is possibly missing from this is who actually paid for the rad hardened CPU, and what a shielded but conventional CPU would have cost to test. The hardened CPUs are mostly born out of military spending rather than space exploration (so NASA would not get the saved money), and arrive with lots of paperwork specifying not just radiation the hardening but 'free' hardening against extreme temperatures and vibration.
An off the shelf CPU would need to be boxed up in the radiation hardened case and then subjected to the relevant tests before launch. It would probably fail and need to be re-engineered and re tested several times to get it right. So the final cost would probably be cheaper, but might turn out to be much higher or even delay things enough to miss launch window and that would be unknown at planing time. Where the rad hardened unit would be a known quantity in terms of price, weight and power from early in design process.
So quite possibly if you are making a family of LEO sats where can afford to have the first couple fail, and spread the testing cost across the rest of the family this can work, and in fact many current generation satellites (particularly cube/smallsats) do go this route.
If you are designing a space probe with a half billion dollar budget and flying for decades then trading a couple of million for enough weight to add another sensor starts to look better. Especially if you can get the computers at less than ticket price and call it a research/outreach project for the agency that designed them.
So this is math that can go either way, depending greatly on the details.