I work in educational IT.
I have yet to see any centralised purchasing cheaper than the individual schools could get the same thing. It's like the old thin-client, fat-client / centralised, decentralised services argument. If you put everything together and run from a central entity, then that entity has to be big enough to handle it all, while also handling all the little customisations for everyone. It also has to work out cheaper, despite being a much larger and taking on all the responsibility and staffing to do that.
But if you push it out to the individual places, everyone ends up with the things they want for the price they want to pay. Sure, it means the uneducated are paying more per seat, but that's because they don't research. Meanwhile, Johnny finds a great deal on Amazon and is reaping the benefits on buying it at 3am on a special deal, in bulk.
State schools all suffered the same problem if they were part of a borough purchasing program. Literally may as well have thrown money out of the window. Rubbish hardware coupled with overstretched support, and contracts that said you "have to" buy RM etc.
I used to break schools out of those contracts by providing myself for ONE DAY A WEEK and doing a better job that those centralised procurement departments. I did that for over a decade before I got bored of the same thing over and over and over again.
Academies were touted as a way around local education departments. That soon was revealed to be a lie as they are either part of multi-academy trusts or owned by entities that bought them with the EXACT same intentions as large government-based procurement departments (NHS etc. inclued) - You WILL use the governor's/headmasters owned company for purchasing everything. They sell a server that's not as good for a penny cheaper than our rival's, but a pack of AA batteries costs ten times as much as just buying one in a newsagent. Once you're in that loop, it costs twice as much to do everything, but everyone signs off because they're getting their 20% from the company that owns it (hint: This is the ENTIRE point of academies, by the way... all the pupil behavioural changes are vastly temporary and just shifting the problem pupils onto ordinary state schools until they can get this process in place, then achievement all returns to what it was before).
Strangely, every single independent school I've ever seen or worked for just uses Amazon, or whatever is cheapest for the product they want. Literally millions of pounds of business every year goes through Amazon from some of the larger schools. I've bought 500+ iPads via Amazon as they undercut every supplier we had, could deliver tomorrow, and offer their warranties. Hell, we even do some business via eBay because do you really care if the phone in that old office for the caretaker is brand new?
When I worked in state schools, that kind of thing (getting the same product simply, quickly and cheaply for the provably lowest price) was frowned upon and not allowed, don't ask me why! You had that "three invoices" junk on large purchases, which just made you choose the best supplier and then find two places more expensive in order for yours to be "best".
And these huge, expensive, prestigious, business-oriented, "jobs for the boys" private schools are all basically going on Amazon and don't require all that nonsense. Literally the time you spend and the money you waste messing about with any kind of central procurement (always subject to corruption) just isn't worth it. There are currently 100+ names plugged into a bog-standard Amazon Prime account at the school I work for... every member of staff @ the school address. Because we order so much, I can just send an Amazon link in an email to the accounts department, CC: in the bursar, who replies Yes/No, and then accounts click the link, buy it, and have it shipped with my name on it. Every morning there are more than a dozen Amazon parcels on the front door for everything from pens and paper to iPads and fenceposts.
My girlfriend, in contrast, works for the NHS where - quite literally - the AA battery story above is true. She's not allowed to claim £1 for a pack of Duracells, she has to go through procurement, pay a fortune (literally 10-20 times as much), it gets delivered a month down the line, gets stolen by some other department in the hospital (very common, because they just don't trace it), and about two months later arrives. By which time whatever you wanted to do has had to had batteries bought for anyway, which you can't get refunded on expenses.
Central procurement is a con and a backhander that only works in an ideal world. Everyone with business sense just buys what they need for what they're willing to pay from where they want.