VDI is many things
VDI, is not remote desktop. It's really a Virtualized Desktop Infrastructure, that is, more like a "shell" that holds applications, the shell and the applications could be coming from almost anywhere. The idea is that the desktop is an abstraction of software that somehow can work together to provide an environment that feels the same as a dedicated OS desktop.
This works well for software that was designed to be multi-user and distributed. Unfortunately, most Windows applications were only designed to handle a single user, single platform mode. This is probably where most of the headaches come in .... and arguably is the biggest hindrance to VDI adoption.
The desktop I'm typing this from is NOT Windows based, nor are the applications. My email client runs on one host and by browser runs on a different host. Yet I can download a file via the browser and attach to email, likewise, I can click a web link in email and it will open up in my browser... this is more like what VDI is meant to be. Seamlessness between disparate applications running on different platforms (and it can change from platform to platform as needed).
So.. VDI is much more than centralized remote desktops... the scope is much much larger.
Biggest issue for me.. multimedia. For that, part of VDI, at least for now, requires a local piece running on the front end, which limits the flexibility of VDI and as mentioned, weakens its security as well. Network introduced too much variable latency preventing most common video formats from working well (you end up with audio/video sync issues, which are too painful for most to accept).