They’re not “dumb” in the traditional old green-screen, thin-net sort of dumb terminals. The WYSE terminals have local RAM, so even if the network is interrupted, whatever is cached in memory will continue to function. I played with distributed VDI at my last company with WYSE terminals, and they worked really well considering it was a hospital system. The nurses loved them; no more clunky desktops.
My current employer, a financial services company, would not likely implement it large scale due to the proprietary nature of the data and the need for 24/7 uninterrupted access to it.
But they’re still dumb in the “if the network goes down so does all productivity” sense. Which is why industry moved away from them in the first place. Also there’s the additional problem that some companies are just starting to learn about that if you store all your data on somebody else’s server they now have all the power in your relationship, deciding they suck and you want all your stuff back can become a major undertaking.