In my experience IT as a cost centre works well
IT was a cost centre in the company that I worked for in the late 70's, with all IT expenses reflecting on the companies' monthly financial statements.
All work for the other companies in the group was charged for on a fixed-price contract basis, with the other companies having the option of employing outsiders. So pencils were pretty sharp when it came to both quoting and delivering.
The first benefit of the system was that all companies - as part of the annual budgeting process - had to budget for their IT requirements, so we had a pretty good idea of what was coming, and could plan accordingly.
More importantly, however, was the fact that all work was going to reflect on somebody's budget. So the 'customers' made sure that everything was specified correctly 'cos, if not, they were going to blow their budget on re-work. Ditto the IT department if we screwed on a development.
And asking the Group Financial Director for extra funds was, to put it mildly, not something one did twice ... 8)