Here's a thought...
>>Why is it ever done...
Because every institution is different - whether it's a university, local authority, police service or whatever. You might think that something like a police constabulary could have a pretty standard business/process model, but talk to people from the Met and from Devon and Cornwall, and you'll find different. Local authorities are even more different - and universities strive to be distinct from each other, it's in their remit.
But this is not an argument for writing one system and nailing endless customisations onto it. It's an argument for institutions who are large enough to spend millions on SAP etc to employ their own IT staff and software developers, who are in daily contact with the institution's processes and people, and can put together a bespoke system which does AND ONLY DOES everything that institution needs. As a bonus, they get to enjoy job security by continuing to develop those systems in the light of the evolving requirements of the organisations. And the organisation gets the bonus that they are not paying for a massive amount of functionality that they will never use, but which makes the software they do use more fragile and harder to test.
Public sector services are not static systems whose entire workflow requirements for now and forever can be nailed down into a single specification and written into a contract - long experience clearly shows that this is a failed model. Instead of spending millions subscribing to cloudy products, and more millions getting contractors to customise those products - and most especially, instead of changing the established workflow of your organisation to match a one-size-fits-all product off the SAP/Oracle shelf - just spend fewer millions employing your own people who understand (and might even feel loyal to) your own organisation, to (continuously) develop a system which works how your organisation needs it to work.
And for those who will immediately cry "But what about all the time which will be wasted re-inventing the wheel???" - the wheel is being endlessly reinvented, in everything from F1 to inertial guidance systems to Swiss watches. Engineers know that wheels need to be round - but roundness is all that wheels have in common with each other*. All the other characteristics are optimised for the application, as good system design dictates - whether it's wheels or software.
*apart from Ferrari steering wheels, but they are just showing off.
You can tell I'm really old, can't you...