Hah, fair enough. Though for once, it isn’t only about catering to motorists. The regulations about standing on this median dividers are usually also part of a policy to curb panhandling. So for example, the signs near me say “No Solicitation Zone” instead of simply “No Pedestrians”, but the effect is the same.
Anyhow, common sense says these aren’t sidewalks, even though sidewalks do sometimes occur in a traffic median:
I do agree that sometimes the paint marks off a gore that doesn’t calm traffic at all and can hardly be called an island. Or if it is an island, it’s hardly a tropical escape: