the "burn-in" argument also perplexed me. tbh I think this was just a unscrupulous tactic that a few manufacturers started using to tackle the problem of product returns. clever, because if the consumer complained their product was not living up to hype as claimed by the manufacturer and sales people, well 'burn-in' would be in subtle way of blaming the consumer for not properly using their product...also gives the manufacturer a healthy length of time that would eat up much of a retailer's refund/return policy. Common sense dictates that if a cable needs a certain amount of burn-in time before performing at its peak, wouldn't this be done at the factory before shipping their products out to the consumer? Why would a manufacturer knowingly ship out a product that is not performing at its best?
As for directional cables.. controversial topic because there are indeed cables assemblies designed for directionality. It is important to distinguish wires versus a cable assembly as a whole. While wires are not at all directional, there are a number of "directional" cables that have specific shielding design elements which must be plugged into a specific component in the signal chain to take advantage of the design topology. A well known example in the pro-audio world is when a balanced audio cable has the shield connected to the ground pin at one end, but not at the other--aka 'floating ground' aka 'ground lift'... (often seen in more 'vintage' components...modern day pro audio equipment tend to have more robust designs and improved components that can take care of ground loops and AC 60Hz hum without the need for external mitigation techniques like this.)
Also, you might come across instrument cables that are specifically designed for one end to plug into something like a guitar and the other end to an amp... the 'guitar end' makes use of a special connector that shorts the tip to ground when unplugged. The amp end uses just a typical TS connector. So if you unplug your guitar while the amp is on, like when a guitar player swaps guitars during a concert, the amp won't be loudly buzzing away due to the infinite source impedance.
Once again, the wires are not directional... the electron flow doesn't care either...but as a whole, the cable assembly is directional to make use of its unique design characteristics.
As for why Monster Cables have a "source" and "destination" labels on their unbalanced RCA "home theatre interconnects" I saw they were selling a while back..? -- only god knows ¯\_(ツ)_/¯
That is pure, high octane, uncut, high grade SNAKE OIL.