Larger diameter tires roll over obstacles much easier (reduced rolling resistance because of larger circumference), which makes things easier on the tire and the bearings. Its why many mountainbikers like to ride 29ers (29" wheels) vs the standard 26" wheels. Easier to roll over logs, rocks, etc. Not to mention, the larger wheels typicall have taller sidewalls which absorb more impact.
Imaging a bowling ball rolling down a concrete sidewalk and over the joints. Fairly smooth. Now imaging a small marble navigating the same sidewalk. It gets stuck in the joints. Yes, this is a very extreme comparison, but on a different scale the science is all the same.
I have nothing against 12" wheels. As I mentioned, I had them on both of my first builds and they worked great. I designed my last build with larger wheels for the aesthetics. The performance was just a plus.
12" marble on left. 15" bowling ball on right.
Yes, it makes a big difference. See the little 2x4 under the front of the little tire. The larger tire can roll right over it.