A Streetcar Named Desire was made in an era where apparently clothing was made of tissue paper, racism was secondary as a staple American trait only to sexism (and misogyny), smoking and drinking (especially while pregnant) as a social hobby was expected of everyone, and violence towards personal possessions was fun and profitable. To summarize, things get smashed, clothing gets ripped, women get slapped, cigarettes get smoked, and coarse language gets flung.
I am thinking the “wifebeater” came about as most shirts probably ended up with this basic shape after the uppity midcentury womenfolk would try to fight back from getting what was coming to them.
Well, not really, but I do think it is plausible that men who are prone to beating their womenfolk learn fast that, when using your arms to both restrain and attack, that they are the only part of you the woman will make frantic grasps at. If you wear a sleeveless shirt, then they are less likely to reach and rip anything important.
Also, it was apparently okay to sedate and commit women for having mood swings (or trying to resist rape). Ahh well, it could have been worse!
Also there is much overacting.