Back in the corporate Windows desktop space of the early 2000s, the Citrix product was almost like magic. The problem it aimed to solve was reduction in cost and effort to deliver applications to users. Instead of managing a fleet of 'expensive' desktop computers, you install the desktop applications on a Citrix server and 'publish' them over a remote desktop protocol. The potential was huge! It was a real challenge to do this at the time. Citrix made it relatively easy to turn any old desktop PC or cheap terminal into a powerful workstation with the resources of a large server. The effect was extremely exciting at the time. A user was assigned a bunch of applications, so when they lpgged into the Citrix client they'd be able to run those applications no matter what device they were on. They could disconnect from running applications and reconnect from another device. There was the added bonus that it worked pretty well over slow network connections (some screen lag, but all other operations at the backend were lightning fast since the application ran in the date center on a beefy server). However, it was expensive. Either you had to have very deep pockets, or you need to dip into you desktop PC budget, fulfilling new hardware requests with existing refurbished PCs or new thin clients (at a lower cost). I never met an IT manager that was willing to do that. If it didn't work out, they'd be stuck with useless thin clients and the prospect of an expensive desktop refresh along with a backlog of applications to repackage and deploy via other means (Windows SMS Server, Group Policy etc). Also, very few people were doing remote work back then.
Citrix tried to pivot into other spaces like virtualization (Xen) but that market was flooded with alternatives, and most companies who used Xen were happy with the free version.
That's something else that had a tendency to kill a Citrix deal. But implementation details are important. In my experience, managers who worked from home loved it because they could get the complete office desktop experience at home. There'd be some visual lag for sure, but visual latency aside, file and print operations were snappy and reliable. Trying to open an Excel spreadsheet over a dial-up network drive took ages. Print jobs were worse. Most installations I saw were POCs that got used as a remote work solution for managers. Any time they decided to deploy an app to all office staff the thing would predictably fall over, because it wasn't sized for that.
My anecdote is that it works much better than any X Windows setup that I have used, and since around 2011 it is either Citrix or RDP on most of our projects.
If we get projects with customers that will rather hand us low quality Dells with 4 / 8 GB with HDD, to access their infrastructure, I will always advocate for a Citrix or RDP based setup instead, due to how bad those laptops tend to be.
Can such a setup have a lossless presentation of the GUI? Personally I really dislike using a modern computer via a lossy video signal, just as a matter of principle. Same reason I'm not interested in cloud gaming even if the latency is great.
Citrix tried to pivot into other spaces like virtualization (Xen) but that market was flooded with alternatives, and most companies who used Xen were happy with the free version.