The weakness is that there is no set price for most things. The suppliers quote for an initial basket of goods. You award mainly on price and set the contract for 3+years. Then the prices that come for the rest of the term can be whatever they want. Usually a cost + x%, but cost is based on their distributors price with no transparency to that cost and no way of holding to account.
Private sector - have a preferred supplier with preferred pricing and then have secondary suppliers. Big deals get quotes from all, otherwise buy from whoever on service, lead times and price. It works better,ends up cheaper overall and you have more love from your account manager.
Other than really large all-nation tenders, frameworks/Public Sector procurement rarely seem to save money in my experience compared to standard procurement in the private sector. Licencing MS software is pssibly an exception to this but your hand gets forced quite a bit and restrictions are quite onerous.