Having witnessed the creation of a centralized IT system close up, I have seen just how disastrous, and ultimately how expensive the results can be. I think the logic behind unifying infrastructure is seductive, but rarely does anyone honestly assess the massive costs, because if they did, no government would ever pay for it. So you put together an upgrade plan that has an absurdly low pricetag, knowing full well that by the time the job is actually done (if it is ever completed), the costs will be orders of a magnitude greater. The critical step to this "unlimited budget via the back door" is to bring the new system up, regardless of how far away from actual completion and stability it is, then immediately shut down the old systems, shred the hard drives and dispose of the hardware, so that no one can ever contemplate returning to the old system as a standby. This is critical. You have to make the cost of retreating back over the proverbial Rubicon so great that you end up being stuck with the new system, and thus with the costs of making it work.
To my mind, the more logical way to approach this is to create a centralized RDBMS, make sure that all the disparate systems at least can regularly vomit out a batch job in one common format, and dump it to the RDBMS. Over time you could conceivably use this new database as a the core of replacement systems, or not , as you choose. I've worked on this kind of system before, puking out batch exports from one system, throwing it into another database and then processing, reporting or whatever it is you want to do, and then pushing changes back up to the systems. It was all done with common shared import/export formats. Now admittedly this does mean having to write code for each system, but that is almost invariably a fraction of the workload of building an entire replacement system and then spending years of ever-inflating budgets, downtime, and in the case of a police force, possibly even risking lives.
But companies like Deloitte, IBM and HP have basically made selling "unified solutions" that inevitably turn into IT catastrophes a vast cash cow, and so long as they can con bureaucrats and politicians into buying into their bullshit, they'll keep making money hand over fist even as the products they roll out remain utter shit.