These puritanical beliefs about gender, nudity, and sex just need to die already. The amount of psychological and sociological harm they have inflicted, and continue to inflict, is simply unfathomable. As is so common, you conflate nudity with sex, but there are so many shades of grey in between. You might even say they're not even on the same scale because sex does not require nudity, and nudity does not require that sex take place (except in the puritanical mindset where the only time a person should see another naked is when they're having sex and even then, we'd best just pretend the whole thing never happened).
Of course it's not your fault, exactly, these ideas are beaten into our consciousness from a very early age. Children have no inherent aversion to nudity, it's a learned behavior from their parents (who rightfully should teach them what is and is not appropriate). However, that teaching often starts creeping into other areas where it's ok to be naked like the privacy of own's room, the bathroom, or the locker room. We're told to keep the blinds closed and cover up because "someone might see you." Our brains fill in the missing dots: it's bad for someone to see us naked, the only time we should be naked is having sex, therefore anyone that sees us naked is immediately overcome with the urge to grope us.
That's simply not the case, and I think you know it. The proposed problem (if it even exists) is not sexual tension, but adults (and supposedly professionals) behaving like impetuous adolescents. The only thing that really marks a difference between a post-pubescent adolescent and an adult is wisdom and maturity, the maturity to understand and cope with things like having your feelings hurt or, as gross as you might find it, that gay guy or that fat girl find you attractive.
So no, DADT is not a reasonable policy, as it is not based in reason. If you actually believe that the policy has anything to do with the "shower problem," you've bought into the bigotry, even if you aren't a bigot yourself. It's obvious to everyone that homosexuals are no less capable a soldier than heterosexuals (and in some cases, more apt than their straight counterparts due to their proclivity to do things like study foreign languages). So tossing a good solider out because they're gay is something most people can use their faculties of reason to say that's wrong and stupid. Oh, but "they might see you naked in the shower," and just like that, people's brains shut off.
Sure, I'll admit that I like the gym shower because it's a great place to see a lot of attractive men without their clothes on. However, it's more on the level of looking at art, or a landscape view on a hike because just as those straight guys have no interest in sex with me, I have no interest in sex with them because there is no reciprocation of that sexual attraction. There's no sexual tension there unless you're the one bringing it to the table. It's the same for most straight guys too: they'll admire that passing beauty in the short skirt but it's nothing for their girlfriend/wife to get upset over. It's not as if the second their spouse turns her back they're going to run over and start hitting on the girl.
I'm glad you brought up the "shower problem" though, because in my mind it really underlines just how discriminatory the policy is. Statistically speaking, your average military man is already showering with one or two other men who could potentially be sexually interested in poor ol' Joe Hetero. Somehow it's not a problem now but it will be once everyone "knows" which among them is interested in dudes? I say "knows" because as other servicemen have pointed out in this topic, it's typically not that hard to figure out ("gaydar" isn't magic, after all) and not that big of a secret anyway. So what you're really saying is that it's demonstrably not a problem but you want to reserve the right to oppress the homos by holding the threat of a dishonorable discharge over their heads. Yet, if a private organization were to take up such a policy it wouldn't stand, not even for a minute.
DADT simply is a bigoted policy, there's just no getting around it (even if it was well intentioned). It's an attempt to put a demographic in a box and label it as "different." Oh sure, we as a culture in general embrace the individual and the different, but there are certain "differents" out there that just don't deserve the same respect or rights, no? That's what you've said after all, is that your "right" to not feel imagined sexual tension is more important than the right of another to be themselves and actually express their existence as a sexual being. I suppose we should also curb free speech because I've probably violated your "right" to not get your feelings hurt by me calling your beliefs bigoted.
It's not even effective because like so many social policies based on placing people into neat little categories, the weakness is that human beings are not so neat and simple. Your fear is a dude checking you out in the shower, and you've sorted that into neat little boxes of hetero (going to stare at the ceiling) and homo (going to drool). The problem is, sexuality isn't black and white and even the idea that a straight guy doesn't take a peak is absurd. Just look at the straight guys that shower at the gym with half a hardon even knowing they're more likely to encounter a gay guy at the gym than most anywhere else in their daily life. Another example of where it breaks down is me: up til now you've probably assumed I'm gay by the things I've said, but I'm bi. Even if you discount the straight guys checking you out the first time you shower together, and feel safe because you've kicked out the openly gay guy, you're forgetting the large percentage of people who have some degree of bisexuality even if they're not far enough towards the middle to call themselves bi like me. Just because someone shows you pictures of his smokin' hot girlfriend and how he loves her tits doesn't mean he doesn't also like your penis.
So to make a (very) long story short, it really doesn't require some imaginary future where there is no sexuality (and I'm sure I'm not the only one who prays nothing of the sort ever happens), it just requires people to treat each other with respect and act like adults. If someone can't do that, they need to be disciplined accordingly, not because they're gay or straight. You might be surprised how far a little respect can go. If you were to approach me as an adult (and thereby demonstrate some respect for me, instead of trying to get me fired behind my back), take me aside, and say "look I know you're gay and I don't really have a problem with that, but it still makes me a little uncomfortable in the shower" I would return the show of respect by working something out, whether that be being in the shower room at different times or simply never looking in your direction (but really, it's a shower, not a sightseeing trip--get in, scrub up, and get out).