I guess the IT department have never heard of MAC address filtering then
. Wouldn't matter what SD card they put in with what ever OS. If the MAC address isn't in the list it can't connect to the network, end of story. And you set up filtering rules for these MAC addresses.
Many places have networks attached to networks. So one router/switch is used to connect the PIs in a classroom, this has the MAC address filtering and rules about sites they can visit if any. Or you can set up time based rules, so if one class need the internet for BBC news then you can set this up. This router is then connected to the main school network, which can then also have rules for this classroom router.
Never under estimate the power of flashing LED lights. Getting kids to write there own program to flash 6 LEDs in sequence is far more popular than trying to emulate it. Its just not the same. I remember writing in assembler a program to do a traffic light crossing. Had 4 sets of lights and even switches to simulate those induction loops.All programmed via a keypad and LED display.
As for theft, you count them out and then count them in. How do you think they do it in schools with a metal work department. You have tags which you hand in for tools and when you need another tool you give in a tag or hand back a tool. At the end of a lesson its easy to spot missing tools and who has them.
Or you could just put the PI in a bigger box. Or screw them down to a large piece of wood or something.
On cost, many schools get local businesses to sponsor them, so why not do it with the Pi's . OK it may mean a teacher going round to various local businesses, but they are more likely to donate 30 or 40 pounds for a single PI rather than 300 to 400 for a basic spec PC. And HDMI monitors these days are quite cheap 18 inch monitors cost less than 100 pounds look on Amazon
they are selling an ASUS 18.5 inch for just under 75 pounds and they are selling a Samsung one for 72. And I am sure you could get an LCD TV with an HDMI socket for less or similar price.
So for less than 150 pounds you have a PI a monitor, keyboard and mouse.
And if a PI gets broken then its much cheaper to replace than a PC.