Is protectionism more suited to large economies? Large economies like the US and China use tariffs as trade weapons while retaining competitiveness because they have the critical mass to encapsulate supply chains and avoid the cost of cross-border inefficiency.

Smaller economies cannot avoid the domestic costs associated with cross-border trade because they cannot avoid depending on cross border trade for supply chains.

Are these statements correct? 

If so, does this lead to divergent trade strategies different sized economies? 

Do smaller countries typically lean towards much freer trade out of necessity, while the largest economies like China and the US can afford and possibly even benefit from protectionism?
This is partially opinion-based. Even if we were able to calculate all the effects, we can still argue if variant A is better than variant B or vice versa.

I don't think that protectionism is suited to any economy. It typically protects local producers at a cost for local consumers. Local producers have less competition on local market, which allows higher prices or worse products, lower efficiency and so on. The winner is not the nation/state. The winner is just the producer, at expense of consumers.

Considering just relations between two states, protectionism damages both of them. It prevents usage of comparative advantages.

It might look like some big players like USA can more or less ignore rest of the world and produce locally everything they need. Well, they probably can, but at some cost. They can ignore manufacturing in China and build phones locally. Those phones would be quite more expensive and less competitive on both local and global market. They can force some advantage for local vendors on local market (at some cost for local consumers), but this does not help the companies on global market. Even with comparable level of isolation, United States could be richer than, say, North Korea or Iran. But they would be nowhere as rich as they are now. 

By the way, there is some evidence of damages of de facto protectionism in large countries: sanctions on Russia. You might argue this is not protectionism. However, it has quite similar consequences – it inhibits international trade. The reason does not matter, the result seems to be the same.

Maybe it would be more disasterous* for a small country. But I don't think protectionism is useful even for large country.

*) in per-capita metrics