Not only is it not one of them... its a game where the community will actively support you if you're running a "challenge build." One guy I ran into last night was playing a blaster, but was going to use nothing but brawl and temp powers to get through content and was having to turn people away from trying to give him millions of influence so he'd have all the temp powers he'd need because he wanted to see how far he could get using only influence he earned himself.
Less extreme examples of self-challenging include things like "Forever Young" (use only your level one powers), "Petless Mastermind" (what it says on the tin) or "Slotless" (i.e. no enhancements in any powers) runs.
Honestly, as long as you put at least one accuracy you qualify for (training, dual- or single-origin depending on level, the vendors automatically include the ones you can use at your level) into your attacks, you'll not be so gimped you can't at least run solo missions.
Also worth noting is that you have an alternate build and a number of free respecs as you level up too. I'm stingy with mine because a lot of times you can build out of a hole and the problem is more the order your powers are taken in (I often make the mistake of not getting my defensive set powers on scrappers until I start face-planting repeatedly because I want something like a full attack chain ASAP... lots of inspirations to carry me through until I can pick up the defensives ASAP fixes it).
Related to this, the level-based power unlocks also serve to help prevent this from happening, or at least give you a chance to catch up if you made some bad pool picks. Your primaries hit a wall at certain points (no new option at level 10, 14-16, 20-24, 28-30, 35+) and you'll HAVE to have picked at least 1 pool power at level 24 simply because if you pick nothing but primaries and secondaries you'll have every unlocked one picked at that point. You'll have to have at least 2 pool picks at level 30 for the same reason. The ancillary/epic powers can be useful in the 35+ range, but they can be skipped too in favor of more primary/secondaries.
And if its STILL awful at that point... I believe you get a free respec every ten levels and can buy more with merits. There's also respec trials you can undergo that helpful players will gladly assist with too if its really bad.
The point is... there's almost no build out there that can't become playable. And the help channel in-game is extremely useful as a resource to do so if you're ever in doubt.