Food delivery apps are not just apps though. In fact, the ones I’ve used are absolutely crap. Most of the value of these companies are in the service, which would change if there is a shared pool of government workers.
If the complaint are the apps themselves, the government could enforce an API that allows anyone to interact with any app with any service. So if you prefer Uber eat’s service but glovoo’s app, you could order from Uber eats using the glovoo app. Just like the EU wants to enforce multi-app support for messaging systems.
The claim that a shared pool of workers would be more efficient I’m not so sure. It depends on who runs that pool. Which history has shown that monopolies (government-run or otherwise) tend to get less efficient because of the lack of competition.
If drivers can choose what order to take at any moment from any service that would basically mean a shared pool. But I believe (I never worked on delivery) that that’s what already happens.