Wrong analysis
Sorry, but you got it all wrong (In my not so humble opinion).
They do not know how much is spent on software because only big projects have to pass stiff barriers (this is: project bids, etc etc).
There is a good reason for this: it is reasonable to have these measures for big & slow to implement projects, but when you need a software tool, you need it FAST, you just can't wait three months for approval. So each department gets its own software using their "expenditure budget". That is the reason for it.
So, if you did what this report suggests, you would need approval for everything you need.. and the company would have to resort to outright piracy to function. You might suggest that you only have to "inform", but accountants need both a figure and a reason to buy things, and some things are necessary but hard to explain to an accountant.
My suggestion: it is OK as it is.