They can do a really shit job of administering payment processes in a transparent and democratic manner before they end up being worse than the status quo where it’s entirely untransparent and undemocratic. Also, governments already have the power to make things they don’t like illegal, so there’s no reason to expect they’d block payments for things they’ve left legal, whereas payment processors currently block plenty of legal things.
Most of the UK’s COVID fraud was from giving out contracts to companies that knew full well that they couldn’t deliver, e.g. a £40 million PPE contract to the landlord of the Health Secretary’s local pup, so it’s not absurd to claim that the point of those contracts wasn’t to save the economy, but rather transfer taxpayer money from the treasury to friends of Conservative Party leadership while there was still something left to loot. There was also lots lost in loans to fictional companies and furlough payments to fictional employees, of which a minority went to small businesses gaming the system, and a lot to organised crime gaming the system and then laundering the money so it couldn’t be traced and recovered (without giving the Serious Fraud Office and National Crime Agency enough budget to hire a workable number of forensic accountants).
The previous government wrote off billions in COVID-related fraud, and this guy got less than forty grand. Either there were millions of people defrauding the government, or the average incident involved much, much more money.
At the moment, they’re already at risk of being removed by the government, who can make them illegal, and simultaneously at risk of being removed by payment processors, who can prevent the stores from operating. It makes no difference to the government whether they’re also the payment processor. They could remove them anyway. Having two entities with unilateral power to remove something can’t be worse than just having one of them.