Which is great. When they work right. Which they don't.
In most games, flamethrowers have three big problems. The most obvious is that they have a limited range. Which is a realistic limitation; flamethrowers in real life can't shoot jets of flame indefinitely far. Even in video games, where we rightfully toss realism out the window if an alternative is more fun, their range is still limited for reasons of gameplay balance. Flamethrowers are meant to be a tradeoff between high damage and short range. A compromise that already precludes these from being a primary weapon, considering how useless they are when you stumble upon one of the cavernous rooms that are so popular in alien Nazi lairs.
The second big problem with flamethrowers is that you can't see what the hell is happening. With most guns you can see the results of your dude-wasting efforts instantly. A guy falls down, or explodes, or doesn't, and within a fraction of a second you know whether you need to keep shooting or change to another target or whatever. But because flamethrowers fill half your screen with fire, you have no idea if you're even hitting the guy you're shooting at, or if he's already dead.
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These two problems could potentially be worked out if you practiced a bit with the flamethrower, which brings us to the third problem -- you never get to practice with them. They're almost always introduced midway to late through a game, by which point you're fighting pretty tough dudes who you can't afford to experiment on, not when you already have an arsenal of useful, universal weapons you trust. And flamethrowers always seem to have limited ammo, preventing you from doing the screwing around necessary to get good with them.
Which is why, every time I (and probably you) get one of these supposedly badass instruments of destruction, we say, "Huh, cool," and toss it over our shoulder.