As a developer acting on behalf of an organization using open source, I benefit from being able to pay the vendor of my choice to host a given piece of software.
If only the single-source author can host it as a service, or you need the permission of the single source author to host it as a service, then my choices are either self-hosting, or paying whatever price the single legal-as-a-service-host wants to charge, at whatever service quality they provide. (The fact they can choose to allow other licensed hosts, perhaps for a free if they want, does not change their monopoly control). It is a form of vendor lock-in, and avoiding vendor lock-in is one popular motivation for using open source.
So yes, this restriction makes something not open source. This restriction also is not favourable to me as a user of the open source software. Open source was always about avoiding monopoly control of who is allowed to do what with the software. Monopoly control of who is allowed to host it as a service is such, and it is more favourable to me as a consumer when there is not that monopoly control.
Now, meanwhile, there are various market battles going on between various big tech cloud providers and other companies providing (previously) open source software. This is also true. Both things can be true.
For the consumer, as the OP suggests, your best bet is when there is software that can be produced sustainably by multiple entities collaborating, instead of a single company.
Now, if that's not sustainable, that's a problem. It's possible that open source is facing sustainability problems due to current conditions.
But that doesn't change the fact that monopolizing legal right to host software as a service is not open source, is rightly not approved by OSI, and is making consumers locked in to that single vendor (or their licencees), which is indeed contrary to intention of open source.