Good post.
I imagine a woman in @police squad's situation might feel slightly more pressured than a man into trying to improve her appearance. However, note my use of "feel" - it would, I think, be mostly in her mind. Most women of my generation (and PS's) have been raised - by society if not necessarily by their family - with the idea that you should always try to look your best in order to progress your career or generally be taken more seriously in anything you do. The entertainment business is the same, only more so! So we would already be making a huge effort in a case like this.
If you want the gig badly enough, I don't think there's anything wrong at all in using "tweakments" (technical term, people! Look it up...). As someone suggests in a previous post, musicians have stage clothes and accessories, choose the right bass/guitar/drumkit for the look, etc. and improving your appearance (in the gym, at the stylist's, at the cosmetic clinic) falls under that same category. However, as that previous post adds, it's keeping up the appearance that may trap you in. Will you have to do botox and dye your hair from now on in order to stay in the band? What happens if you don't? Would it be like meeting someone on a dating app and discovering they put a 20-year-old photo of themselves on their profile? Will the band have fallen in love with you in the meantime and accept you as you are?