IDK why you think that "4 equal sides" is the same as "sideways square".

You can (and frequently do) have equal sided diamonds that aren't "sideways squares".

Seems like your main issue is geometry.

People would definitely want to elongate the top and bottom sides

Which is fine. As long as they elongate symmetrically (which most would do), they're still four equal sides.

There's no way a human is going to draw 4 equal lines

Yes they would. In fact most would, I'd wager.

Sounds like your concepts struggle is comprehending that "four equal sides" isn't the same as "four equal vertices".