As you suggest in your OP, driving TO Strasbourg is not the same as driving IN Strasbourg. It's a medieval town with narrow, one-way streets, canals and bridges, and for tourists, it's very walkable. We did, in fact, rent a car on the outskirts of Strasbourg (after three pleasant days in Strasbourg) to begin a tour of the "wine route" to the south.
Presumably you know from your business driving that garage stalls are very small in Europe, and the passages in the garage are much narrower than in American garages. I noticed on my last trip to Washington DC that (surprise) many garages are closed there on weekends .... so we shouldn't think of Strasbourg as a second-class city!
You might want to check for an Umwelt Plakett [sticker] (I mean, at rental time... ) on your rental car before entering German towns and cities. I don't know if France has urban restriction zones. My own feeling is that five hours of driving is much more stressful than using public transportation, but that's a matter of opinion. There certainly have been some posts here about annoying highway congestion in Germany.
Not to change the subject, but if you plan to take a boat ride on the middle Rhine, the car will be an annoyance. But you can use the fast, comfortable, frequent train to get back to the car after boating from Bingen to Boppard, for example. Make sure your luggage isn't visible while parked.
