The entire premise of a placebo-controlled study is to see if a treatment works better than something that produces no effect.

Both the placebo and treatment have placebo effects. By comparing the treatment to a placebo, the placebo effect is cancelled out.

Whereas, comparing a treatment straight to non-treatment, leaves it unclear how much of any perceived benefit the treatment has was due to placebo, or the specific treatment.

You may have been saying that, I wasn't sure what "no effect" was emphasizing.

An alternate means of getting the same comparison is to have treatment and non-treatment applied without any patient knowledge of either, when that can be done. Which works, and is more straight forward from a measurement standpoint, but is ethically unacceptable.