I suspect in most cases, you'd be able to recycle control data from a previous study, and hope their placebo effect should be similar enough; or that your treatment effect is substantially stronger than optimism.

But given the kind of conditions we'd be likely to use this methodology for, I don't know if the placebo effect has a strong effect on outcomes.

A “placebo effect” isn’t really applicable in this case. It would be optimal to have a control for patients, something like giving them a pill with every ingredient aside from the drug, but this is likely not going to influence something like brain cancer. Brain cancer will not be influenced psychologically, and there is enough data to know on average how long patients with this cancer will survive. In a phase 3 trial it is important to get enough patients to participate for good statistics, and to do it as ethically as possible. To do this, you can just leave out an active “placebo” arm of the trial.