The user doesn't have to be logged in as that account, per se, as they can specify whichever credentials when they create the data connection. So, UserA logs into Flow.microsoft.com, and they create a flow (which means that UserA is the Owner).When they connect to SharePoint, the connection might default to use their account, but they could just click a little drop-down menu and select to use a different set of credentials, at which point they could enter the username/pwd of the service account.
I certainly agree that any system is going to be a hassle. Even having a service account isn't necessarily better than just having the new owner sign in and update the credentials. The non-service account method also has the benefit of getting someone from the dept to look at the flows and get rid of unnecessary ones. While flows that use service accounts will always run successfully, the downside is that they will keep running successfully for years, even when they're no longer needed or useful.
In my first reply, I mentioned logic apps. To bring that subject up again, if you check out Microsoft's guidance around this, they clearly state that Flow is for "Self-service", while Logic Apps are for "Mission Critical" scenarios. And, one can take an existing flow, export it as a logic app and then import it into the azure service.
So, perhaps the workable scenario is that UserA leaves, and ManagerA compains that UserA's flow is failing. IT then converts UserA's flow to a Logic App and configures it to run via a service account. No further issues are experienced with that particular flow.
After all, another scenario is that ownership is given to UserB, who goes to update the Flow, but doesn't really know how to use flow, and in the process they break the flow. Since Flow has no undo capabilities and no version history, UserB calls IT and asks them to rebuild the flow, despite the fact there is no documentation and no one else really knew exactly what it did. Both ManagerA and UserB then spend the next 6 months compaining that IT isn't very helpful.