But still - sandals are supposed to show your feet (possibly signalling something about accepting some discomfort), and you're defeating that.
I see. For me, sandals are light, let my feet breathe, and minimally confine my toes - while socks protect against rubbing and abrasion. Comfort and functionalism trump fashion rules, here.
When you say function, you mean, "it protects my feet from broken glass and concrete, is easy to put on and take off, and feels good." You've defined 'functionalism' to mean the effects of the item on you rather than including its effects on others. The functional uses of fashion (being attractive, being liked, being approachable, raising the aesthetic average) are very powerful in any location with people around.
Some fashionable alternatives to sandals with socks: boat shoes such as Sperry Top-Siders, loafers, or generic slip-on shoes such as Va...
Yesterday I attended a meetup where the discussion turned to fashion for a time (because apparently the mini-camp participants were given some instructions on fashion as a useful part of instrumental rationality). (Unfortunately none of us knew much about the topic so the discussion turned into "how can we find an expert to advise us for minimal cost?") It was mentioned that dressing "badly" can be a useful signalling device, and some examples were given. Here's an attempt at a more complete list of possible signals one might be sending by dressing "badly".
The idea here is, if you do decide to start dressing "well", know what you're giving up first. (Of course you're also giving up possibly implying that nobody taught you how to dress and you're not sufficiently strategic to have thought of learning it yourself. Or implying that you don't have the mental, financial, and/or social resources to keep up with fashion. A lot of signaling depends on what your audience already knows about you, or can infer from your other signals.) See also Yvain's related post, Why Real Men Wear Pink and comments there.