I do not agree with the word 'waste'.
At the client end, my students are already using a variety of devices of their own with non-Microsoft interfaces. I have no doubt of their ability to cope with client PCs that had (say) Gnome Shell or Unity running on them, certainly no issues with XFCE4 or one of the Gnome 3 'remixed' interfaces. We already use RDP to access more exotic software such as Adobe/Autocad &c. The musicians and media people have their Macs for Logic and Final Cut.
As always it comes down to the business systems, and daring to be the first institution to change. If Greece is still at the stage of putting building-wide wifi into their schools, well, it strikes me that there is an opportunity to try a different approach possibly with lower total cost.
Anything over and above that _is_ waste.
(FWIW, I dislike the term 'training'. Someone else said this first, but I agree: training is what you do to dogs, education is what you provide people.)
Open source would have caused Greece to spend a part of that money inside the country, employing local specialists.
For example, it's worth paying for Windows Server just for how much easier it is to run large deployments of PCs and users from it using Active Directory, group policies and suchlike. Rather than hacking something up in Linux or whatever.
Your argument assumes that the commercial and open-source offerings are equal in quality and features, when in fact the major commercial software is far superior.
My argument isn't an abstract commercial vs open-source one: it all hinges on the quality of the software: if Microsoft suddenly open-sourced their entire operating system and productivity suites, they would still be the top choice in my book.
But I argue that for large-scale development it is feasible to develop a Linux distribution that will fit schools better than Windows ever does. With everything school workplace needs, installable in one click.