But yes, historically the awful screeching around corners was because BART used cylindrical wheels. It's also, apparently, why they can't run all night -- the tracks need nightly maintenance due to the grinding.
https://www.apta.com/wp-content/uploads/Resources/mc/rail/pr...
https://www.bart.gov/sites/default/files/docs/New%20wheel%20...
May it be for the same reason? If so, then the fix seems straightforward.
https://books.google.ch/books/about/BART.html?id=ubbwDwAAQBA....
The cylindrical wheel decision is closely related to the decision to use Indian/broad gauge, which was expected to provide a smoother ride as well as allowing more support equipment to be mounted under the car where it would produce less vibration.
Both are decisions that have not stood the test of time, although the choice of Indian gauge cannot practically be reversed. But I think the discussion around this often pays the original designers far too little credit: BART was intentionally a highly innovative design with numerous aspects that were somewhat experimental. BART's automated control system, for example, was such a debacle that BART initially operated with signal towers and the control system required nearly complete replacement. But it was a completely trailblazing design, and the same missteps would have to be made somewhere. BART was used once again as a test platform for an innovative radio control scheme in the 2000s, evidence of which can still be seen mounted trackside on the SFO wye.
Many lessons learned from BART's performance have contributed to later designs around the world, including notably the DC Metro which was built just shortly after by some of the same contractors.
It would probably be very expensive, and might not have ROI, but couldn't you lay narrower gauge rail in between the current rails, then modify or replace rolling stock to use the smaller gauge... and once done, remove the old broad gauge rail?
Looking at some random BART rail images, laying the new rail would be difficult; some places have equipment between the rails, other places have concrete between the rails. It would probably need to be a very long project; early stages could just be verifying which sections would be feasible to add narrower gauge to and making sure new construction would allow for it and when rework is already happening, consider working room for narrower gauge into the maintenance. You could really only progress sensibly once at least one line was nearly ready.
I guess the question would have to be, would all the expense and time it would take to switch to a narrower gauge, be justified the improvement in user comfort (I assume) and benefits of using more standard equipment.
It would be a lot of expense, for not a whole lot of benefit in the short term, and BART probably doesn't have enough money with reduced COVID commuting trends to even think about paying for something like this when they could instead build more rail and get more butts in more seats.
This is wider than most metro trains (especially 19th century systems), but BART isn't a metro system anyway.
[1] https://en.wikipedia.org/wiki/Loading_gauge#Standard_loading...
My recollection is that this was also related to running (relatively) high-speed trains on elevated tracks in windy areas, and so wanting additional lateral stability.