As a default, it is a perfectly rational and safe assumption to never use a connecting link. You will never have a failure because of that decision. But properly sourced and assembled they are safe and useful.
One of the interesting things you learn hanging out in yards around really big boats is that in larger sizes, chain comes in "shots". One "shot" of chain is 15 fathoms, or 90 feet. On large yachts and ships, anchor chains are all assembled from "shot" lengths using riveted "c-links" to connect them.
Properly made, drop-forged, heat treated, c-links should be as strong as the chain itself. The issue is: how do you know you have a properly made one and not some brittle cast steel POS from an anonymous Chinese steel mill?
With any "mission critical" shackle or other such metal part, I have always tried to source through an industrial supplier who specializes in such things. That means NOT West Marine, who seems to buy from whoever is cheapest that week. I have a love/hate relationship with WM. This is one of those areas I go somewhere else.
Good suppliers who sell parts that are used to lift heavy loads over people's heads tend to be REALLY careful about where their parts come from. They know they are one lawsuit from being out of business. They always have documentation all the way back to the original mill heat that made the steel. And you will pay for that care!
A downside about even the best such connectors is they tend to have very thin galvanizing, and need to be inspected and replaced on a schedule because they rust much faster than the chain they are holding together, especially the rivets that were peened to hold everything together.
Great Guana Cay, Abacos, Bahamas