I'm pretty sure the whole point of the perks system, and the removal of classes, was so that you could play any/all character-builds with one character...
Nope, just the opposite in fact, as simple logic dictates. The point is to encourage specialization, since you only have a limited number of perks. So even though you could max out all skills, the perks are what make them powerful, and there's not enough of them to fill out more than a few skills.
The idea was
perfect. You can be a Jack-of-all-Trades (ie, decent at a wide range of skills). Or you can be a master of a select few skills, and poor at the rest. It gives a reason to specialize, since specializing will make you more powerful in certain skills than if you try to spread yourself out over all skills. It avoids all characters gravitating towards Master-of-All when at high levels.
It also gave you the flexibility to try various class styles
early on, without risk of ruining a character because of a few "bad" perk choices, and to let you naturally fit into a desired class role as you play (a few misplaced perks won't really harm your character in the long run). It was never designed to let you play any and all character types, or to switch half-way through... if it was, then perks wouldn't have been so limited, and if perks were unlimited (or re-selectable), then it wouldn't have been terribly different from Oblivion's skill leveling.
The only fault, really, is that some perks could be better designed and less superfluous. But overall, it does the job its designed to do pretty admirably.