I don't think it's vile. I don't think it's misogynistic. I don't think it's 'fat-ist', considering that several of the 'walk of shame' girls had model figures themselves. I have done the walk of shame several times. Once wearing a ballgown and carrying my shoes and stockings. 'Walk of shame' is an amusing term and nothing more. The only shame in it is that you will be wearing unsuitable clothes, last night's make-up and might well have sex-hair. The 'shame' part of it is not something that anyone I know takes to mean that it's shameful to have had sex. It's about looking a state.
It's silly to ask why there are no men doing the walk of shame! A man in last night's party attire is likely to be wearing a shirt and jeans, or a suit. Hardly something which will turn peoples' heads the next morning. So it wouldn't work with the concept.
I do think it's a bad advert, though. The woman at the end was still clearly doing the walk of shame in last night's clothes. It's hardly like her dress is standard daytime attire any more than the other dresses in the advert.
YANBU for liking it.