No, it doesn't. At the end of the day you can only use one weapon at a time or wear one suit of armor at a time. That there is something else you could be wearing hardly matters from moment to moment.
Part of the issue is that it is a single player, single character game and there is only one 'trade' to begin with ... wasteland adventurer. Most of the skills wouldn't constitute a 'trade' to be a master of, but simply represent staples that everyone who wanders the wasteland would have to become familiar with to avoid an early death.
The only two skills I can think of off the top of my head that represent whole trades are 'medicine' and 'science', which cover a whole lot of ground in theory but only add up to a few skill checks during the course of a game. Maybe repair could be added to that list, though science is just as likely to be used for any mechanics based checks.
As to character diversity from game to game, capability-wise they aren't likely to be very diverse anyway. Okay, so that one uses energy weapons instead of guns ... big deal. They both aim and shoot at make critters dead. This one wears chinese stealth armor where as that one used combat armor and stealth boys. I'm floored with the diversity.
Oh, but this one is good at bartering! That means instead of having a million caps in his pockets, he has a million and a half! Just think of all the extra um ... mole rat meat he can buy.
The only 'balance' in a single player game is the character vs the environment. If encounters are too easy, it's probably not because the player character has too many different weapon skills so much as it is because the weapon skill and weapon he's using at the moment is too effective.
While I'm all for choices and consequences, I'd rather them be handled story-side. Helping A makes friends with A and opens up opportunity A1, but makes you an enemy of B and closes opportunity B1, for example.