If it boosted all frequencies it would just increase the overall signal (= louder). But it will do *nothing* of the sort (at least not as you're proposing) - all an amplifier will (should) do is apply gain to the signal (that is, make the signal larger); it does not magically improve (or transfigure) the sound quality. Depending on the interaction with the load it is presented, and relatively speaking, it may act on the frequency domain to an extent, but an EQ is a better bet if you want "big, dramatic, night and day" changes, and if you're looking to change something on the time or radiative domain - look at the speakers/headphones.
Impedance is not a "quality" or "performance" spec, despite what a lot of marketing suggests. It's just a characteristic of a given driver - some will be high impedance by nature, some will be low impedance by nature, and there is no rule of thumb that one is better than another. Higher impedance doesn't actually even require more power (power requirement is determined by sensitivity and your target SPL (which should always be <85)), but it *may* require relatively proportionally more voltage (which is why some portable devices have problems with some high impedance headphones).
Generally with headphones sold for at-home use, the designer/manufacturer doesn't have to care either way, because the assumption is (or at least was, for many years) that you're plugging them into a stereo receiver or integrated amplifier which will drive its headphone jack with the "main" amplifier section built into it (with resistors in the way, to protect both ends). Usually these devices will put out a few watts per channel for headphones (which is more than any ten people should ever need; seriously). However that's changed in recent years, and people have started to want to take their headphones with them and plug them into things like CD players and iPods (which have inherently limited voltage swing, due to their battery power). So this is where low impedance headphones have an edge.
It's all relative, basically - if you're talking from the perspective of an AC powered integrated amplifier or CD player, it really truly doesn't matter what specifications your headphones have; if you're talking from the perspective of an iPod, it's better go with low impedance and high sensitivity, to get the best out of the device (and the less it has to put out, the longer the battery lasts); if you're talking from the perspective of a marketier - oh good lordy, your headphones better be at least one trillion ohms, and your amplifier's output better have negative impedance across it, so that you can show fantasy numbers with a ton of 0's and tell the customers about specifications (that have no actual bearing on their lives) and move more units.
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