It seems it is not exactly/easily possible for discourse-hosted instances: Support embedding Discourse in an iframe - feature - Discourse Meta (apparently JuliaLang had similar issue some time ago), but a potential existence of such option was mentioned in that thread (and of course with self-hosted instance everything is possible).
As for whether this is a good idea: it would be ok-ish if we had a list of sites that we can allow-list (presumably mybinder.org, localhost (? - this might be problematic, but is how most users access JupyterLab!), etc.), but we won’t be able to enlist sites for custom deployments. Maybe it would be safer to just change it in JupyterLab.
Please let me know what you think.