I've seen actual psychiatrists suggesting meditation or yoga as additional ways to help with certain issues (eg anxiety) along with medicine, and the benefits of say, just conscious, controlled breathing as is involved in both are obvious to anyone who has a temper.

I wouldn't be surprised if the idea that it's completely useless because it can't be scientifically observed in a traditional sense is highly correlated with people who think that mental health issues aren't real in general.

It's dismissed like any other woo woo bullshit: strong claims, no evidence.

Where's the evidence that yoga and meditation accomplish the effects of sleep and how strong is it?

There are studies on this, and I see they've been updated a bit. It doesn't seem to replace sleep due to Delta-waves during deep sleep, but can be used over time to maybe reduce the need for sleep. Enough sleep is of course important for clarity of mind and for releasing toxins and stress. In the West we often suffer from chronic sleep-deprivation, so meditation may help in that as well as ensuring enough rest in order to recuperate.

https://www.artofliving.org/us-en/meditation/sleep/meditatio...

You don't really need studies for this when you can have experiential evidence through own practices, which is much more important for an individual than external studies.