Yes, Unix was paid, but companies didn't switch to Linux, they switched to Windows.
So the cost of Linux doesn't have anything to do with this.
The reason why Unix workstations died was that Windows became good enough and PCs we getting good enough.
Windows PCs were cheaper than Unix workstations, and if they are good enough then there is no reason for a company to pick something else.
Then we have the last nail in the coffin, Itanium.
Itanium was supposed to be the future, Intel marketed it hard enough that companies that had previously developed their own CPUs decided to switch to Itanium and stopped developing their own CPUs.
Then when Itanium proved to be a crap shoot, they had nowhere to go.
I didn't mention Windows because I don't remember any serious workstations using it. PCs did become good enough but it still wasn't the professional workstation level. Though if we're talking about computing in general, Windows has been the king ever since 95 or even 3.0.
I worked in local government that used Unix workstations for GIS (Graphic Information Systems) - mapping of the local government's property boundaries and many other layers. The DB was held on a DEC Alpha, and it was all very pricey, albeit very good at its job. ESRI ARCGIS, etc
When the time came to replace, they moved it all to Windows. The workstations were beefed-up PCs running NT4.0 and the DB was on a server with NT 4.0 server. DEC was gone by then, absorbed into Compaq, Alphas were discontinued, and no-one wanted to migrate to SUN or HP.
I worked on HP Unix systems, SGI Iris etc: Running CAD on then till around '96 by then the big CAD players had ported to Windows NT and everything got switched to a PC. Because by then PCs had caught up and were much cheaper than running the Unix software and hardware