Consensus appears to lean to this being a labor-saving replacement for splicing wires with a connector. Spliced wires held together with a screw-on connector cap gives a good connection, backstabbed wires have spring-loaded connector that gives a small area of connection which is failure prone and can be a fire hazard (it heats up). Replace the backstabbed switch with a regular switch and use connectors. This does not explain why you can't seem to find the breaker for this switch.