Is it really necessary to loosen/unmount handlebar while packing bike? Reading multiple advice on how to pack a bike in a cardboard box for shipping, I have always read to "remove the handlebar" or alternatively "loosen it and rotate it by 90 degrees". 

Since my bike has a straight handlebar (like this one)


I wonder why not simply removing the front wheel and turning the handlebar and the fork by 90 degrees?
Two reasons, one major and one a little more subtle.

Majorly, most adult bikes won't come close to fitting in a standard, non-oversize bike shipping box if you just turn the bars and fork as you describe. What counts as oversize and how much more it costs will vary depending on where you are in the world and the carrier, but you'll need a significantly bigger box and that will generally be more expensive.

Second, if you have the fork turned in the box, only one fork end will be contacting the bottom, which will prevent the fork from being able to sit flat on the bottom of the box and will cause loads on the box to have more of a tendency to side-load the fork, the direction it's weak in. The normal way of sticking a plastic fork block in the fork ends which then sits flat against the bottom actually does a lot to keep forks from getting crushed.