I think there's also a perspective worth evaluating whereby trying to explain unknown stuff, we over-complicate in the process. 
In that regard, if we want to keep it as simple as possible, the explanation/comparison of Bitcoin to the Dollar and sats to the cents (or whichever fiat currency they are familiar with), is in that context an extremely easy one for a new user to grasp because it conjoins the familiar with the unknown. 
And maybe, that's all we really need. 

It just needs to be clear when a user is onboarded (Note, I don't think we need to SHOW the fiat value, just convey the comparison). 
Also worth noting as Bitcoin's value rises, sats may also be less and less attainable - And I think that's where your thinking comes in of keeping to a singular name which is understandable - Keep it simple, whilst allowing expansion. 

I think it'll be a wait and see game, because sats really did gain a lot of traction with the introduction of Lightning, and rightly so.  

And personally I think all this will come very very naturally - Up until relatively recently, the bitcoin unit was very attainable by the average person. In the present, not so much, and yet we're seeing more and more adoption - A string being pulled in seemingly opposite directions. It'll work out in the end.