They certainly frown, but only if they know you're doing it. Don't lie if they ask, but no need to offer it up. You can also book without using your frequent flyer info to be safe.
A->B->C most likely is more expensive to the airline than A->B, but cost to the airline is just one factor in determining how much the airline charges the consumer. B could be a more desirable destination than C, and so people are willing to pay more for trips to B.
Not sure - perhaps the airline is promoting that route or that route is already popular. Often the "C" segment takes you to the Caribbean or to Las Vegas. Price is not always correlated with distance flown.
If you had bought the trip you actually wanted to take, you would have paid more. Further, it would have left a seat open on the second flight which they might have sold to somebody else, making even more money still.
Of course, the second flight probably isn't 100% sold out, and you might have gone with a competitor or not taken the trip at a higher price. But they don't necessarily see that, much like music labels don't necessarily understand that every instance of piracy is not a lost sale.
First, you probably shouldn't do this as the first part of a roundtrip ticket, as the airline can cancel your return if they think you're abusing the system. That may not be important for many people, but it's there.
Second, if something goes wrong (bad weather, can't find a pilot, whatever) the airline may reroute you through a different city, completely screwing up your plan. They don't really care where you connect, and as far as they know neither do you. If you book, say, JFK->LAX->SFO and the engine falls off your JFK->LAX plane while sitting at the gate, they might move you to a route like JFK->ORD->SFO, and saying, "but, but, I was going to leave the airport at LAX and skip my flight to SFO" is probably not going to get much sympathy from the agent.
Don't they give it back to you at the end of the flight when that happens? In my experience, only bags checked during checkin get routed through connections.
lol I am the aforementioned co-founder. This is definitely a flight booking hack with costs and benefits that have to be weighed. I don't personally book this way for savings of just 10-20 bucks. When it's something like $80 in savings or more (I saved >30% on my last flight), you start to think maybe the expected value will come out positive, even with all risks considered.