It's mostly a matter of principle since I assume internet searches to be closer to a postcard than a letter. I could write about some health-related thing that is potentially embarrassing in a postcard, because I doubt the post office cares, or that my mail carrier reads postcards, but I'd probably prefer to put it in a letter delivered inside an envelope.
It seems like better practice to learn which sources tell mainstream, reliable information about things like bordetella vaccines and regular nail clipping, before I get really emotional about an anal gland that needs to be expressed or before my person finds a weird lump on my front leg.
More seriously, back to human medicine, I am disappointed that so many reputable medical information sources with read-only information prevent Tor network users from accessing their information even though malicious Tor users aren't able to add misinformation.