What spiritual goal, if any, is served by modest dress? Or is there some other purpose to modest dress than to serve a spiritual goal?
I think that "spiritual benefit" is subjective, as is "modest dress." So whether or not dress that is perceived to be modest serves any spiritual goal would vary from culture to culture and from person to person.
From what I've seen, many Muslims see benefit in dress they perceive to be modest in that it supposedly decreases the chances of undesirable temptation and/or lust, for example. Others dress modestly because of belief that it is mandatory in Islam, regardless of whether or not they think it is necessary to avoid temptation, lust, etc.
Also, I know Christians who wear hijab mainly because of social considerations and not out of religious conviction. Like any dress code that is common in any given society, wearing hijab may or may not be due to religious belief in its having spiritual value, which in my opinion underlines the cultural influence in determining what is or isn't "modest" dress code.
It seems to me that cultural traditions and already existing taboos play a part in at least some notions of what constitutes "modest" dress. I'd go so far as to say that said traditions are sometimes held and preserved so fastidiously that they come to be seen as sacred or spiritual in nature, even if they weren't initially viewed as such. That's not to say that is necessarily a negative thing; I don't think there's any problem if people choose to wear a certain type of dress. It's only when it's forced on them that it becomes an issue.
One thing I've noticed is that a seemingly major criterion to determine whether someone is dressing modestly or immodestly across several cultures appears to be what people generally expect women to wear so they would conform to prescribed notions about how they should act or handle themselves in public. If a woman wears something that would be out of keeping with one of those notions, she's considered "slutty," "indecent," etc. From my experience, people who care so much about how women dress in public don't seem to pay nearly as much attention to men's dress codes. There are still some socially unacceptable dress codes for men that would be seen as "inappropriate," of course, but those don't seem to be focused on as much as women's.
So, another aspect that I think influences some perceptions about the spiritual value of modesty is how the latter is supposedly tied to sexual temptations. If someone views sexual desire as a bad thing or as something to avoid, then they may try to curb that through different methods, including close observance of "modesty," "appropriateness," etc.
Personally, I think it's arbitrary and unnecessary to draw any kind of causal relationship between dress code and sexual desire; it seems to me that no amount of clothing in the world would compensate for poor self-control or lack of respect for other people's boundaries.