I went out a few times to drive on the empty roads but the only reason I went out was to explicitly drive, I wasn't actually going anywhere because there was nowhere to go.
You could still visit friends and family, public parks, or even have private parties. And since you weren't being physically pulled into work, you could visit distant friends/family or even go on vacation and stay in a hotel. I'm not saying you wanted to do any of these things given the pandemic, but it's fallacious to imply that you were only stuck at home due to government fiat.
As far as why they worked, I ran into enough people who thought such a recommendation had the force of law (and I wasn't going to correct them). At the time I had a bifurcated living situation and was concerned about doing the commute, but looking into it I could continue going about my routine as usual.
On the other hand, that this has become such a trope indicates that the stay at home suggestions ended up working. People who weren't paying close attention to details thought the suggestions did have the force of law, without there actually being such laws.
(As an aside, I sympathize with small business owners and think "lockdown" is appropriate (albeit hyperbolic) to describe business closures. It's the society-wide usage of the term I'm talking about, where it's implied that people were not allowed to leave their homes. A few counties in California were the only instances that I'm aware of)