The EDD (California) did process millions of applications (or so they claim), but more than a million are still outstanding.
The problem seems to me to be in their mission objective: they view every applicant first and foremost as a potential "wellfare queen" and attempt to prove that as a fact (17 years ago, in the aftermath of the Internet bubble burst, I lost my job as well, applied for unemployment insurance benefit and the phone interview I went though was as bizarre as unpleasant -- I didn't get to the phone interview this time 'round).
I wished they would rather operate like the IRS: after preliminary, automated checks using tax records (was the person employed by employer as claimed, is that person now employed?) hand out the money and perform selective, random in-depth audits asynchronously.