For example, I don't think it would fly that they could say to the EU: users who want a third-party browser just have to enable root access and lose access to all Apple services and authentication
Well. I guess they'll have to choose between opening it up like every other company does or acknowledge that it's a separate pay for service then.
They do a lot of that kind of thing and my answer for all of it is the same: Open it up to everyone or acknowledge it's a pay-for cloud service that has nothing to do with the actual phone OS. If people have root they can (and will) develop their own services that won't need that which would comply with the DMA.
Hell, just releasing my own personal code as open source — auditing it, decoupling libraries, removing internal stuff, it's a huge multi-week effort for me to do. For any company with as much code as Apple, it's pretty daunting
Perhaps if they had opened parts of their infrastructure much earlier, they wouldn't be legally compelled to do it now, and have to invest significant resources to do so.