And that's true -- it is a good thing. It's valuable to players that they are able to express themselves in these ways in these games. However, there are many things that would be valuable to players, but which everyone agrees should not be added to a game due to the costs. I argue that for the most part, customization falls into this category.
The problem with customization is that it is reliant on massive amounts of content, which basically means that balance is impossible. It's similar to -- and usually includes -- the problem of "perpetually adding content" to a system. If the system has enough stuff that you can "customize" it based on your personal preferences, then it definitely has way more content than it needs.
Of course, there seems to be a great deal of demand in the marketplace for this sort of thing, with a game like League of Legends making more money on some of its customization features than it has with anything else. As we all know, though, "what makes for a strong design" and "what makes more money" don't always align. In case it's not already clear, I'm particularly concerned with the former problem.
One caveat would be that in a system where social interaction is more important than gameplay, such as perhaps some types of "social games" or MMOs. In these systems, it might be wise to have some kind of customization features.
Secondly, it's usually okay to have some level of customization so long as this doesn't affect gameplay. For instance, having a differently colored costume for a character probably won't have much of a negative impact on your game. Non-gameplay stuff only starts to matter once your gameplay elements start to become less visually clear, which again reminds me of Team Fortress 2. When this game was released, it was beautiful looking. All the in-game art assets were consistent with each other, and you can listen to the TF2 developer commentary to hear about how they carefully considered stuff like character silhouettes, which is the first way human beings are able to tell objects apart from each other.
As most people know by now, TF2 is now all spammed up with thousands of hats and other weird accessories, not to mention dozens of extra guns, some of which are only model-swaps with no gameplay difference. So, the game is vastly less clear now than it was on day one, and that has turned many players off from the game.
What about a case where "customization" is actually gameplay-essential, as in the case of equipping items in an RPG? My answer would be that if there's some system there which is so un-strategically interesting / flat / trivial, that you can leave the decision to some kind of personal "preference", then it's dead weight on the system. Classic example: do you want +1 attack, or +1 defense? Obviously, you need both; there's no way to use strategy to decide which one to get, so in this case you could simply choose based on your personal whim. The problem is that the system is asking you questions whose answers are actually meaningless.