Skiplagging, particularly on a carrier you have no relationship with can also make for cheap premium seats.
Let’s say I wanted to get to FRA and Lufthansa has J seats for $2,500 RT direct, but if I can live with just overhead baggage I could instead book two one way segments that end elsewhere for…half the price? Done.
Example: DFW-FRA-TLV and skip the TLV segment and FRA-DFW-ABQ on the return and skip the ABQ segment.
I don’t buy flights anymore but it only ever worked domestically for us — I can fly with a backpack but my better half, on the other hand… 
Sometimes an overnight layover forces your bag onto the baggage claim at your intermediate stop. Not always a certainty though.
Skiplagging too often with the same carrier is a good way to get yourself blacklisted from flying them at all for a period of time. And, as you noted, not an airline you have a relationship with (status, miles you care about etc.)
And be careful skiplagging with TLV as a destination if you actually want to go there someday. Great way to get flagged by Israeli security…
Yes definitely, and true point regarding TLV, this was just an example.
But they have a great sense of humor, I hear!