How Skyrim plays depends on a character's strengths and weaknesses. In theory, not being able to do everything with a single character improves the game's replay value. Also in theory, being limited in your perks allows you to enjoy a particular play style longer by preventing you from acquiring powers that render a play style obsolete. Take a thief who must sneak to survive because his combat skills are mediocre. Give him weapon prowess and you could negate his need to sneak.
Making all perks available to a single character might not be so bad, though. Even if all perks were accessible, you could still limit your character by choosing not to take perks. You could also choose to avoid using certain skills. If you did decide not to limit yourself, becoming a master of all skills takes a lot of time, which means it can be a long time before two different characters start to play the same.