^Like I said, it's just what they did in the comics of the time. Batman was usually drawn as Batman, and was rarely seen without his cowl unless there was a specific story reason for it. Batman: The Brave and the Bold, which was a series-long homage to the Silver-Age Batman, took it even further: We never even saw Batman out of costume or heard him referred to as Bruce Wayne (aside from a couple of flashbacks to his childhood) until more than halfway through the series, in episode #37 out of 65. (Which made it a much more potent moment when he finally revealed his face in a retelling of his classic original confrontation with Joe Chill.)
There's also the in-show mechanics of it -- they didn't change costume themselves, but rather there was some sort of mechanism that changed their clothes while they descended/ascended the Batpoles. So it was kind of an all-or-nothing approach, either in-costume or out with no middle ground.