No one right way to play but maybe a right way for ease , less likelihood of injury to neck, wrists, shoulders etc.

I think you've answered this yourself. In the sitting position, playing off your left leg with neck about eye level you can feel how much squarer everything is up and down the body. Shoulders and hips square. 
in fundamentals Lisa advises a shorter strap with the guitar higher across the chest. Again, for the mechanics of playing the guitar. Cool can come later

As beginners we will put strain on new muscles ,tendons etc as we learn to play. we can minimise the strain by a good posture. As we progress strengthen and toughen up we can make slow adjustments until we can play in a multitude of positions even the coolest of cool.

In the beginning we need to learn to play the instrument , the look can follow on. Style over substance.

I play seated and changed early on to the left leg, foot raised by a stool  after suffering severe neck spasms which may or may not have been brought on by physical stresses before my body was accustomed to the guitar practice.

You can find YouTube vids explaining why the correct alignment saves back pain etc.

hope this helps

Dave L