Why haven't we banned Capita
The continual expensive failure of Capita to provide reasonable service, let alone good and efficient service, really should have led to a multi-year ban across all public bodies from signing new services from them.
I'm not going to pretend that £130m/year all goes on the IT system - it'll include recruitment teams, marketing, assessment, career guidance and other things - but fundamentally this is a basic HR function. Companies with under £130m/year revenue, let alone HR spend, manage this just fine and it's trivial to scale.
Start giving smaller organisations some of these tasks. Boost the economy, not Capita shareholder dividends. Or if you really are going to be stupid enough to sign Capita, make sure the contract includes performance penalties. Lots of them. Shit, you'll make money on it.