"but the security team doesn't care about optimization, summarily blaming sluggishness on lack of SSDs. Are they blowing smoke?"
They're blowing smoke to a large degree. SSDs are lot faster however as anyone who ever bought one knows, they are not capable of speeding up the movement of a large number of files \all THAT much since the Windows Explorer builds in a huge overhead around every file transfer and this is what takes files so long to be copied from point A to point B. So to the extent that you're opening a lot of files, transfering their bytes into RAM, then closing them,. it's still going to take a significant amount of time.
Sure, if you have one HUGE zipped file then SSDs are all that and a slice of cake, as advertised, but not much of what you're describing involves moving large files to and fro. Processing many files you;re going to see some speed up but mostly it's the processing itself that takes the time.
Yes, it's faster to read and write with an SSD but you'd be shocked how often the actual speed of reading into memory and writing out to disk has to little to do with how fast something happens on your computer. I was.