If you reduce the sidewall height on the tire at the same time, the diameter and circumference of the total assembly remains the same.
In some cases, very low profile tires are used to put visual emphasis on the larger wheel, and the total diameter/circumference is actually smaller. This is the equivalent of raising the final gear ratio.
This is basic geometry.
Of course, the sidewall reduction has side effects (no pun intended):
I lived in Italy and drove a Lancia Delta which had narrower performance sidewalls. This was before the ultra narrow of today. I should have taken a hint when I bought it as the owner said he would replace two tires that had sidewall blisters.
This was in Napoli and a lot of the roads were pretty rough. The only time in my life where I hit potholes and had blowouts. I was buying a tire every 2 to 4 months. In the 3.5 years we were there I bought more Than 2 complete sets. I tried Pirelli, Dunlap it did not matter, sidewall blisters or blowouts. Never had any tire issues with it.
Eventually We got a Fiat Tipo which had regular tires and drove it most of the time.
Low profile tires also suffer from a narrowed range of acceptable tire pressure to avoid a sudden catastrophic failure. Under-inflation alloys excess sidewall flex to generate heating and exceed allowable materials bending stress. Over-inflation increases likely-hood of pot hole or road debris inspired belt damage, by not sufficiently distributing the impact energy.
Concentrating the spinning mass at the periphery of the wheel/tire combination for the same overall diameter or weight, would increase the applied force required to accelerate or brake the wheel, and thus the vehicle. This increases affects forces on drive-line or braking components.