While I can only speak for myself, I imagine many users forgo using Google for privacy reasons. While I have managed to escape the Google ecosystem almost completely, YouTube is the most challenging service to avoid since it has a monopoly over its content.
I believe working on this problem would constitute a major improvement in user privacy in practice. I imagine there might be some privacy benefits to loading the results in an iframe, for instance content can be proxied through Google's nocookie API. Quoting from their documentation:
The Privacy Enhanced Mode of the YouTube embedded player prevents the use of views of embedded YouTube content from influencing the viewer’s browsing experience on YouTube. This means that the view of a video shown in the Privacy Enhanced Mode of the embedded player will not be used to personalize the YouTube browsing experience, either within your Privacy Enhanced Mode embedded player or in the viewer’s subsequent YouTube viewing experience.
If ads are served on a video shown in the Privacy Enhanced Mode of the embedded player, those ads will likewise be non-personalized. In addition, the view of a video shown in the Privacy Enhanced Mode of the embedded player will not be used to personalize advertising shown to the viewer outside of your site or app.
- Google Support Documentation
The documentation on this feature seems to be fairly sparse, but I think it is safe to assume it is better than using youtube directly.
Iframes also support some native sand boxing capabilities, it would be interesting to see if any of these could be applied to limit potential information leakage.
