Supposedly the reason to go to 5w-30 vs 10w-30 was indeed better fuel economy at cold start. IIRC, GM wrote papers justifying this.
Its a reasonable thing. While we know that we can see fractions to single digit percentage changes in MPGs in controlled conditions changing by a few cSt at operating temperatures (e.g. 20 vs 30 vs 40 wt), the differences at cold start could possibly be bigger when the oils are fully cold. The issue is that notionally the vehicle doesnt spend a lot of time when the oil is fully cold/thick, but for city drivers that may be a bad assumption. Further, getting oil to flow faster in the engine is always a good thing
So there really is no downside, assuming shear stability and no VII issues.
The issue really is that like most engineering, there are tradeoffs and diminishing returns. Going from a straight weight or even a 10w to a 5w- likely has a benefit, but it may be getting less and less at reasonable temperatures and use.
From an engineering analysis POV, you WILL see an MPG improvement assuming the oil is actually less viscous at the startup temperatures of interest. Whether youll see it or not is another question...