I mean something different: no one has ever measured a critical volume, your dp/dv flatlines at the critical point, i.e. there is no driving force to make the fluid balance out the naturally occurring fluctuations, indeed relaxation times go to infinity at the critical point. An EOS only gives you the thermodynamic equilibrium value, attained when you let it sit for times much larger than the relaxation times.

The Widom line(s) are somewhat arbitrarily and ambiguously defined, so I'm not a big fan (pseudo boiling all the way!), but the whole point there is that there is no phase equilibrium at supercritical conditions. However, just because we never observe supercritical liquids and gases simultaneously in equilibrium, does not mean they don't exist. They absolutely do and do lead to a phase transition between liquids and gases - just not coexisting.

This also means that your other comment needs a revision: we absolutely do have something akin to boiling at supercritical conditions, even with macroscopic effects, such as the (subcritical) boiling crisis <> (supercritical) heat transfer deterioration.