I was going to ask, because I was under the impression that commercial airlines are mostly flown by auto-pilot anyway.

The captain or co-pilot whoever is outside, has the code to open it

In the US (and other countries) the door is locked but there is a PIN to open it that the cabin crew have access to. Even then, there's a time delay to the door opening, during which people in the cockpit are notified and can reject the request.

That means that no food cart should ever be needed to block the door. But the cockpit should never be totally empty anyway, as surely only one of the two crew should be using the toilet at a time.

(Note: I'm not a pilot, just a reader of Admiral Cloudberg's blog.)

The door being blocked additionally by a food cart may be an additional security step. Some airlines treat having the flight crew needing a bathroom break very seriously when the cockpit has to be opened in flight (ex sending passengers back to seats if they try to go to the front bathrooms, closing curtains, lead staff up front on standby, etc).

Here's the cockpit locking system on Airbuses, for what it's worth as well: https://www.youtube.com/watch?v=ROIH3KCEIvs

There is a button that sounds a 'request' chime, and a code that when entered starts a timer and alarm that once stops, releases the door momentarily for an emergency entry. The crew inside can still disable that unlock, if they are conscious (and this is some kind of attempted hijacking with knowledge of the code).

The FAA (US) requires this. EASA (Europe) adopted this rule in 2015 after the Eurowings incident but it was rolled back in 2016.

The kinds of planes you're thinking about, yes.

From what I understand, it's affected by two things:

1. The regulatory side, driven by the size and complexity of the plane. That in turn affects potential number of passengers and typical hiring arrangement (pay-per-seat vs charter vs personal use). If you google best single-pilot aircraft, you'll see things like the hondajet, pilatus pc-24, and citation cj2/3/4. Nothing larger or more complex than that.

2. Insurance requirements for particular flights. If you're hiring out a plane to carry other people, you need a different kind of liability insurance. That insurance might require you to have two pilots even for a small plane (like a stereotypical primitive prop plane, or a previously mentioned small jet like hondajet or citation cj2/3/4) that might in other situations be legal to fly with a single pilot. Or, for someone like an executive with hefty personal injury insurance, that person's insurance might not cover them if they fly in a plane with a single pilot.

That's not to say that all "for hire" flying requires two pilots. Consider small prop planes for sightseeing, or skydiving, or island hopping the Caribbean. Unless something's changed recently, you won't have two pilots for those kinds of flights.

The reason I brought up personal insurance for passengers: CitationMax (certified ATP pilot who flies his parents around in their private jet) on youtube has mentioned that his father's personal/executive insurance requires him to fly with two pilots. Even when they had a cj3+, they added a contract pilot when his father was onboard. Now they have a citation longitude, which is large/complex enough that it can never be flown with only one pilot, even if no passengers are onboard.