You should. While it's true that your primary residence won't be counted as an asset in order to qualify you for Medicaid, they can and will place a lien on the property if you ever enter into a nursing facility (and maybe in some other situations). This allows them to capture the proceeds if the house is sold while you're living or (in some states?) from your estate when you die.

Older families should strongly consider placing their home into some kind of trust or transferring ownership to a descendant before this becomes an issue.

“Will want to because of potential downstream inconveniences of” and “will have to in order to qualify for” are...very different things.

That's true, but I don't think most people would put, "the state sold the house my mom has lived in since 1972 and kept the proceeds" in the "downstream inconveniences" bucket. It's a pretty big deal! The whole point of getting approved for Medicaid is that you won't have to go broke paying for your healthcare (at which point you'd qualify for Medicaid, anyway).