Surely "ideology" implies doing something out of the ordinary? As far as I can tell, ideas that have come out of TfGM so far seem in line with similar organisations elsewhere. Nothing earth shattering.
That's not what ideology means

It's about following a set of principles or beliefs.
Buses in Manchester haven't been run commercially for over 3 years now anyway. Even outside Manchester you have a fare cap running until late 2024 at the earliest. That makes neatly 5 years of direct subsidy. At what point do you stop pretending that buses are commercial?
At the point that bus companies are simply paid a management fee for service provision rather than taking on the commercial risk.
Intrigued why commercial transport operators should know best. The goal of a private company is to make money. A bus company makes money by running services. But those services that it wants are the ones that make the most money. If it doesn't make money, it goes. Doesn't matter who it affects. If a service doesn't make money, the operators don't want to know. The social good of providing services to everyone are irrelevant to them. Why? Because they're a business! If it wasn't for subsidies, huge chunks of our public transport system wouldn't exist.
Incidentally we are one of the few countries in the world where most of our major cities have public bus services run like this. Even in the USA - that bastion of capitalism - you'll find that bus companies in major cities are publicly owned, and publicly run. We're an outlier.
To haul this back on topic, the concern is that you end up with decisions that reflect, not what customers want or need, but simply reflect political or ideological considerations. So in Greater Manchester, they've adopted the sensible approach on cross-border routes. That is a positive. Better integration into Metrolink will be a positive, where buses and Metrolink positively co-exist and provide network connectivity, with many local routes simply acting as feeders into Metrolink in Bury or Rochdale or wherever. What we don't want is to see a series of Gateshead-type nodes that artificially distort bus service flows. More Heworths, fewer Gatesheads.
Commercial bus companies do pursue what the market wants - that's true. Also, I can't and won't defend some of the operators who mismanage their businesses - looking at Arriva and First in this respect. So again, it's not some Animal Farm world of absolutes in that something is "Good" or "Bad". Remember that the deregulated market was based on the ability to support socially necessary services. Greater Manchester had the ability to do that but has been undermined (as have all local authorities) in having their finances regulated and reduced by central government on the altar of austerity. Again, the allure of cross-subsidy seems attractive but we don't want to see a situation where good bus services are pared back (as in London) in order to support a growing proportion of peripheral "nice to haves" out in the sticks.
Interesting that you mention the US as an example of public ownership. They are indeed...and if you've travelled on them, you'll know what an experience that can be. Far scarier than getting a bus in the UK! I might also add that being an outlier is less pronounced - once upon a time, you had the UK vs. most bus services in Europe (and indeed, public services) being directly owned and operated by local authorities. Of course, Veolia, RATP, Arriva, Abellio have managed to create substantial businesses based on the movement of services to being outsourced so a place for capitalism does exist!
I passionately want to see better services, appropriately and sustainably financed, across the UK.