Why does a single player game have to be balanced?
Because there isn't meaningful choice when the correct choice is absurdly obvious.
However, before we get confused, I want to clear up some terminology. "Balance" should refer to the adjustment of player options
such that multiple choices are, or at least appear to be, viable, making the correct choices non-obvious. If you're not talking about two or more player choices, the concept of balance doesn't apply, because the player in the driver's seat isn't weighing
multiple choices within his or her head. If we're talking about a player versus AI situation, we shouldn't be using the term "balance" to describe it, but instead more accurate terms such as "difficulty" or "pacing."
So if what you really mean is "why does a single player game need to have difficulty?" then the answer to that is: if there isn't a set of player choices which involves some form of failure state, then even wrong choices win, thus balance no longer matters - there is no meaningful choice. I guess to some perfectionists out there suboptimal loot-per-hour is a failure state, so it's worth noting that "you have died" screens aren't the only way to create the appropriate tension.
And yes, these are two forces that work against each other. On the one hand, having one choice be a clear winner is no fun because choice is essentially automatic; on the other hand, having no choices be losers is not fun because choice is irrelevant.
While this is all true, there's an even stronger requirement for Balance (actual balance, not just difficulty) between various PvE builds.
Strong PvE builds are able to obtain resources much
more quickly than weak PvE builds. This game importantly has several options to invest resources into future returns, such as getting a stronger weapon to kill faster, or getting MF gear.
On top of that, trading is competitive, and strong PvE builds are thus able to trade better as well. (Granted, this argument is only true while certain builds are desired over others, and while they have specific desired gear/resources. Bad balance certainly aggravates this.)
As a result, if you really
want to play fun, wacky builds and test the game out and have a good time, the first thing you should do is play the most broken, boring fucking thing that everyone is talking about. It's a huge tax on player time and choice, and it often leads to people being unable to "gear up" what they want to play within a temp league, or to being tired of partying with the Same Fuckin' Build every time.
Anyway... subclasses are cool.