The regular advice is "protein shake ASAP after workout", but I'm
wondering where this is coming from.
As a guy who has a financial interest in the supplement industry, I can tell you where you're getting that message from: supplement manufactures and retailers. The idea is to make you think that unless you consume a given product you won't be maximizing your "gains".
And for perspective, what if I had to wait 4 hours every time?
Specifically, how would my muscles cope with longer periods
(consistently) of no protein intake after a heavy workout?
You probably have enough protein in your blood at that point. Follow my math on this. With the exception of whey, which is rather fast-absorbed, most natural sources of protein take somewhere in the neighborhood of 3-7 hours to be broken down, so protein is slowly being released from your gut, broken into amino acids, and sent into your blood.
So if you had ham and eggs at 6 in the morning, even by noon (6 hours later) you still have amino acids moving around in your blood. If you slammed a whey shake at 10 in the morning, you have a lot of amino acids rushing around come noon time.
The general idea for "eat protein every few hours" is to have a steady state of amino acids rushing around through your blood since repair work is done slowly over a period of hours and days.
Directly answering your question:
You probably are not going long periods without protein. Provided you have a balanced diet, enough protein, and eat throughout the day (don't sweat the details on that part), you've got amino acids floating around able to keep up.
I'm a big believer in supplements, but they're not magic beans, and I don't like how the marketing spin makes people think that if they don't use a tub of powder every day they'll shrivel up to a 120lb weakling.