Ho. Lee. Crap.
I do IT for a major regional hospital chain, and all this time, I thought it was just my company that was this fucked up.
What you're talking about is EXACTLY what happens. Doctors, managers, vendors, whoever CONSTANTLY show up with junk hardware and software, throw it at us, and expect us to support it. The organization is so bloated around the middle that no one has the authority to tell anyone else no. We have hundreds of Access databases, SQL servers running on people's desktops, and apps that we've never heard of turning up constantly.
And it all happens so fast, and we're SO understaffed (4 IT staff for 2000+ devices in my hospital) that we don't have a prayer of keeping track of it all.
And the understaffing is a problem in and of itself. The organization as a whole has around 30K total employees, of which 700 are IT staff. Probably 10% of the IT staff does next to nothing. Another 30% does nothing beneficial to patient care, or actively makes patient care harder. 20% are redundant management. For example: my particular part of the company, staffed by 4 IT grunts such as myself, has 4 managers directly over me: 1 team lead, 2 Project Managers, and an Account Executive. All of whom often want conflicting things done at the same time. Finally, the last 50% of IT here is made up of everybody else working their asses off to make up for the rest of the crap.
No wonder heatlh care costs are sky-high. IT is indicative of the whole mess... the company is a gigantic mish-mash of hacks thrown together at the last minute to satisfy the newest bureaucratic requirement, public opinion, expensive doctor, negative news story, malpractice suit, or demands from the board or rich donors. There's no way anything like this could run efficiently.