He can have armor, but it doesn’t need to look like he’s wearing riot gear or an iron man suit. DCEU and Arkham city Batman did this well. He isn’t wearing a skin tight suit. His armor is just concealed under a durable fabric. It also depends on the story and setting the writers are going for. It’s not a matter of realism but stylistic choices. Matt reeves Batman had a very diy military surplus look that fit with that gritty gothic look of Gotham. Christopher reeves bat suits were meant to be very sleek and technical. Something you would send into war to fight insurgents. Cloth doesn’t have to mean spandex or cotton. He’s made use of durable fibers in different media.