The hand sanister is a nice example.
How would they know how many they have?
One way is to keep a database of them - even something as simple as an excel sheet. That excel sheet needs to be saved to a file server - so you need IT people to install and configure the server.
It needs keeping secure so that hackers cannot use it to 'jump' onto more confidential files so it needs patching and the security permsissions need setting up and then maintaining when someone joins or leaves.
Those permissions require a Active Directory to maintain them centrally so someone needs to build, configure and maintain AD.
You'll want to access that spreadsheet from your work PC so there needs to be a LAN/WAN network connection - they are different skills to server and AD maitenance so now you have at least 2 IT bods.
If you accidentally delete that excel file one day you're going to want to get it back without sending someone round counting sanitisers, so you need enterprise level backup solutions. That requires someone with the skills to be able to manage backup software which on the scale of a hospital is massively complex.
It will need storage to be be able to save backup copies. One copy is not enough, you will want version history which requires frequent backups and several copies. That a storage admin you need to build, configure and manage storage kit.
Those servers and storage all need housing somewhere where fire or floor (or just a hot day) won't damage them. So now you need to run a data centre or rent space in one. If you run one yourself it needs staffing 24/7. If you rent one, you need a contract negotiation.
All those IT bods need managing so that they have support and development - otherwise they are going to leave and someone else will come in who doesn't know the system as well and there will be no one to show them who knows.
They will also need their share of a HR system, development system, leave request system, timesheet system and maybe more. Each of those systems requires some of the same considerations as above, so the footprint grows bigger.
Assuming you want all this work to carry on even when people are on leave, you increase the workforce a bit more to provide that cover - and the footprint grows bigger.
Or, you know, you might skip much of that because it really does seem like overkill for hand sanitiser, and just ask Doug to pop round and count them every so often 