Ouch. Sorry that happened to you.
So, tire experts, confirm or refute my hunch, which--being a hunch--is based on no data. I've always been glad to have 18s, figuring there's a lot more rubber between the wheel and a pothole than is the case with 20s. And that extra rubber gives more "give" or shock absorption or protection or whatever. 34,000 miles, and a few pothole encounters, and goin' strong. But is that a real thing?
It isn't actually the 18s vs the 20s, but for a given car with options that are keeping the rolling radius the same it works out that way.
Damage like the OP has happens when the impact is severe enough that the tire is completely collapsed and energy is still being transferred directly to the rim - that's what bends the rim, but the extreme flexing to get there is what blows the tire.
A tire with more distance for the rubber to flex can take a harder hit before taking permanent damage. You're seeing the trend to rubber bands lately partly because of looks, but also because of handling. Tires with a lot of flex protect against road damage - but they also flex a lot in a turn and on hard acceleration and braking.
So it's a matter of finding the right balance, but I'd rather give up a little handling performance to get the durability, so I don't trust anything under about a 45 series tire (the second number in the tire definition is the height of the sidewall as a percentage of the width of the tread, and is probably the best actual thumb rule for the tire flex. My light trucks growing up had 75 and 85 series tires...)