I wear glasses and I have no problems, I have astigmatism so I cannot see far distances and I am in the Infantry. As far as the thick funny looking glasses go I do not know, in the past you where given a budget, so if it was $50.00 with lenses and you have no extra cash to upgrade then you will get the cheapest pair, the thick funny looking ones. Also in the US, they may have to wear them to conform; a US soldier would have to answer.
The problem arises when you have to wear a gas mask, then you cannot wear glasses, or you will have to get issued gas mask glasses, contacts are handy but as an infantry soldier, the solution freezes in winter, and you get a lot of dust in summer, so they are out.
Also many times in summer, more so when it is raining, I took them off, they where wet and if you are speed walking you sweat so they were useless, all wet and fogged up. But the guy's with perfect vision were affected as well; it is hard to see distances in the rain.