It's not rocket science. TfL specify a tightly specced and measured performance regime covering a wide range of attributes. They are also relatively hands on in terms of checking what is actually being done. I think they have learnt a load of lessons over the years from PPP, DLR sub contracting and also how they track and measure performance on the bus network and Tube. None of it is perfect and it's clear there have been a range of issues over the years. TfL has also had the ability to spend its way out of certain issues although that's pretty much gone now.
The important difference is that TfL know they are the client, they act like the client and they have their own means of measuring, checking and analysing whatever the operator may submit or claim. TfL are also able to take a long term view as they have secured the right to operate these services in the long term and can therefore take a view longer than one franchise. The operator is also not obsessed with the revenue bottom line although they have an incentive to minimise ticket fraud. The main danger for TfL is an operator may become overly obsessed with costs in their regime leading to some unsatisfactory decisions. I assume TfL have tried to reduce that risk by ensuring there are minimum standards across a wide variety of attributes to prevent the cost base being eroded. I suspect TfL would be happy to see "acceptable" cost savings and probably has a mechanism to share in the benefits but would need to agree to any such savings. Overground and TfL Rail aren't perfect by any means and I think the contract with Arriva is going to struggle compared to how LOROL performed but I'd rather have TfL's approach than what we see on other urban rail networks in the UK.
The Dft say they are NOT the client despite speccing the franchises. They say everything's down to the TOC or Network Rail even though DfT dictate rolling stock policy and deployment and obviously control NR's budget and spending. DfT say they are "hands off" with franchisees and I suspect they are on a number of things like properly managing the contract, verifying performance is what the TOC says it is and actually getting out there and seeing what the heck is going on. Meanwhile in a lot of unhelpful ways the DfT are far too "hands on". It's no wonder there are issues on a number of franchises when the body that actually is responsible for railways, despite its denials, doesn't know what it wants to do or why.