How and why do we compare drugs to standard of care during clinical trials?

From what I understand about clinical trials, these days a drug is often not merely tested against a placebo to see if it has any effect, but against the current standard of care drug to see if it has a greater effect than what’s currently available.

Seems to me that there’s a glaring problem with that, but maybe I don’t understand correctly.

Say that drug x is the standard of care for some type of cancer and we’re testing drug y against it. We find that drug y only puts 20% of people into remission while drug x does 30%. It’s not more effective, so we don’t bring it to market.

But what if that 20% of people who were helped by drug y are among the 70% who wouldn’t have responded to drug x? Wouldn’t it still be valuable to bring drug y to market as a second option for people to try if drug x doesn’t work for them?

Am I misunderstanding how this works? Can someone explain this process to me?