They're not altogether useless. They keep the sun off your face and neck, which can be very useful in some climates. In Australia, where I live, a hat is now a compulsory part of every school child's uniform, and they are expected to be worn in the playground, because we have very high rates of skin cancer here. I don't know if that will translate into adult fashion or not. It might be too early to tell.
I suspect watches may diminish but will always be around because they signal status in a way that hats don't.
It's not (only) a symbol of wealth. Within limits, any reasonably classy watch will do. But wearing one is self-selecting into a certain group - someone who cares about the details, cares about time, wants to make a good impression.
I don't want to overstate the point, but I definitely notice a nice timepiece, just like I notice well cut clothes, cufflinks, good shoes, neat hair, an elegant piece of jewellery, any number of things people can do to make an effort. It's signalling, and it does make a difference, for better or worse.
I suspect watches may diminish but will always be around because they signal status in a way that hats don't.