Why are Schengen and non-Schengen flights mixed at Corfu airport?

The political salience of immigration, technological changes, and concerns over terrorism have all contributed to a much tighter border enforcement but it's important to note that borders in (Western) Europe have long been much more open than in some other parts of the world. I remember the (pre-Schengen) time where many border posts between France and Switzerland were open or border guards would just wave you through after a cursory look. The police was not actively seeking people staying illegally and removals were reserved for people who came to the attention of law enforcement for other reasons.

Enforcement was based on formal or informal risk assessment (which might include racial profiling). Arguably, this is still the case: I don't have stats to back that up but I have the feeling that the French customs and police spend more resources patrolling the border with Italy or checking long-distance busses than checking the length of stay at international airports or Eurostar terminals. In that context, a potential loophole in a remote airport that requires quite a bit of money and ingenuity to be properly exploited isn't going to be a concern.

Recently, I have seen a similar setup in Toulouse: there is a Schengen terminal there but not all Schengen flights use it. I assume it's due to operational constraints: lack of suitable gates, quick turnaround between a non-Schengen flight and a Schengen flight when there is no dual-use terminal. The first thing the border guard asked is where I was flying to and they presumably treat passengers accordingly. I don't remember whether they checked my boarding pass but they could easily do that too.

The main issue is the inconvenience to travellers within the Schengen area, as one of the objectives of the whole thing is to make it easier to cross borders. After security, I expected a hassle-free walk to the gate and was surprised to stand in a (short) queue and be subjected to questioning by law enforcement (to be fair, being a citizen, the questioning was very cordial and superficial, but I tend to find that intrusive nonetheless).

On the other hand, I don't see any scenario in which the exit stamp is a huge issue. Exit stamps play an important role in the regulations but much like speed limits and traffic lights, enforcement doesn't need to be airtight for them to serve their purpose. There are countless reports of haphazard stamping in the Schengen area and many travellers can testify that border guards do not always spend time checking all the stamps in a passport.

And what good would your exit stamp be? It might be useful to hide a longer stay when you come back to the Schengen area but in the meantime you still run the risk of getting caught within the area without a coherent paper trail. Then, before coming back, you also need to find another loophole to leave the area, lest you show up at an exit border check with no way to account for your date of entry (and, worse, exposing the fact that you actively tried to dodge the rules).

Finally, if you are prepared to have a confederate walk with your passport just to get an exit stamp, they could easily do that at any number of airports in the Schengen area. All you need is a real or fake boarding pass, no need to actually fly to another Schengen country. They could then reenter on their own passport, directly or after flying inside or outside the Schengen area, it doesn't really matter.