What's the point of filing the FBAR in addition to one's US tax returns, which include Form 8938 ("Statement of Specified Foreign Financial Assets")?

From the IRS page on the difference between the two:

The Form 8938 filing requirement does not replace or otherwise affect a taxpayer’s obligation to file FinCEN Form 114 (Report of Foreign Bank and Financial Accounts). Unlike Form 8938, the FBAR (FinCEN Form 114) is not filed with the IRS. It must be filed directly with the office of Financial Crimes Enforcement Network (FinCEN), a bureau of the Department of the Treasury, separate from the IRS.

So, the difference isn't whether they cover the same information or not (they're similar, but not identical) but who they are filed with.

Separately from that, there are differences; as you note, FBAR has much lower limits (aggregate value of all accounts reaches $10k at any time in the year), while Form 8938 only kicks in at $50k (single) at the end of the year or $75k at any point in the year. The linked page lists all of the differences.

Since they are filed with different entities, and they have significantly different rules, you must file both - the US government doesn't do very well sharing between divisions (even divisions of the US Treasury), and so you file paperwork twice rather than filing it once and having the information sent over.