How does such a service have inherent data flow problems? Especially since the NgbModal service IS built on a component that implements pretty much the same thing as react-bootstrap's Modal.
It uses components, it is not built on a component - the goal is for it to be able to manage multiple modals and some situations that are impossible to do right with component-based modals such as reusing a backdrop (I argue that multiple modals is a bad pattern, but it is a high demand user feature). It also allows flexibility into hooking into the lifecycle in the future with knowing when the modal renders, starts or finishes animation, and similarly for when the modal closes.
With component-based modals, you end up with bad APIs for these use cases, as well as less control over your state.
Yes, if you build a component based api that supports multiple modals, resuing backdrops, lifecycle hooks, that api would suck and be a real pain to build a service version on top of.
A React component should not be trying to do all that, but merely produce the appropriate HTML for a modal dialog. That produced HTML can equally be used to build one-off "are you sure?" dialogs, a modal service, or what have you.
With component-based modals, you end up with bad APIs for these use cases, as well as less control over your state.