First of all before I go on, apologies if any of the upcoming post is inappropriate for the forum - I don't want to post in appropriate content, but at the same time it is relevant to the thread. If any of the references are deemed inappropriate please feel free to edit out.
I think it just comes down to being more comfortable in ones skin, and more comfortable with ones sexuality.
For example when I was in high school, none of my friends would dare admit to engaging in certain 'self satisfying' actions. In fact people were so embarrassed about it that they would accuse others of engaging in this, in order to insult/embarrass them.
After finishing high school once you get to maybe 20-21 eventually one guy admits to it, and before you know it everybody opens up about it and admits they were doing this all along. Suddenly everyone is like "phew", I'm not a weird freak after all!". From that point on, nobody has any problem discussing this with their mates.
Even at that age though, nobody in the group would ever allow themselves to be seen naked by another mate. That's just weird. If any two friends admitted to that happening, everybody in the group would kill them with homophobic insults and the like, regardless of the circumstances behind it.
But then once my mates got older (maybe 29-30) suddenly they all start openly admitting to their willingness to 'share a girl' and have absolutely no shame about being naked around each other in the process. Based on stories I've heard, I'd say most of my friends have probably been naked around each other by now, and none of them care.
Not really my scene myself, but it's interesting how guys seem to care less and less about things like this as they start to get older. It seems all it takes is for 'one of the boys' to try something like this, then share the experience with the rest of the group, and then everybody else becomes more comfortable discussing it. Before you know it, it becomes 'fair game'.
When it comes to public 'revealing' it probably has a lot to do with self consciousness about ones equipment. Allow me to explain in the most modest way possible.
Many years ago, studies were done to try and identify what the average size of a man was. These studies revealed that the average man had a 'tool' of around 7.5 inches in length. Given that many men are avid viewers of adult films, most men already have an unrealistic perception of what is 'normal' in this area. So the whole 7.5' study probably fell well in line with what most men felt was the average for a man.
The problem is that this study was later found to be flawed. The problem was that the study was voluntary, asking for men to make contact and volunteer the information. Naturally the men who are well equipped are going to be more inclined to volunteer this information, while men who are not are probably going to be quiet about it. Likewise, many men are obviously going to lie, or at least "stretch the truth". This all means the statistics are going to be heavily skewed.
Some years later another study was done, but this time a very large sample size of men were brought in to the laboratory and actually measured. This time it was concluded tat the average size was actually closer to 5.5" - a vast difference to what the first study showed.
So why is this relevant?
Because as the information above would indicate (and other studies have also been made on this) the average man believes he is poorly equipped (i.e. significantly below average in size) when he is not. This creates a false sense of insecurity among many men, even though they'd never admit this among their friends.
Since most younger guys are still very much in the dating game (and hence very concerned about reputation) many younger men are probably very self-conscious about walking around nude in locker rooms and the like, just in case somebody they know happens to walk in and see them...and that news suddenly gets around to their friends (or worse, girls) that they are poorly equipped. This self consciousness probably explains why a lot of men of younger ages prefer to cover up. I'm sure you'll find that many of the younger guys who are unusually well equipped are probably perfectly happy walking around sans-towel.
As for older men, it's a different situation. By the time most men are 50 or 60, they probably no longer care about any of this. By this time they have probably come to terms with the fact that at the end of the day, nobody (especially other guys in a locker room) really CARES how well equipped you are. Everybody is just there to work out, and go home. So because of this they have no problem going about their business in their birthday suits.
Now surely there would be exceptions, such as men who have been brought up in strict/modest households. But I'm sure for many, this holds true.