Increasing AC frequency vs increasing number of phases
it seems that you will no longer have a alternating voltage between -xV and +xV but by switching between phases you can get a voltage alternating between +xV and 0V at twice the frequency.

That is incorrect, but it's an understandable error.  It would appear you're perhaps being confused by the &quot;goofy&quot; situation of US domestic power to electric cookers, water heaters, laundry dryers, etc.
First, let's consider the fundamental facts of AC power: the AC component of a signal necessarily alternates around its ground, and such alternation is inherently symmetric as a matter of definition.  Any offset or asymmetry from ground is a DC component, and while that might locally exist, it cannot pass through transformers widely present in a grid, so in a conceptual analysis it can be ignored.
So what is present on that clothes dryer outlet?
In a typical US residence, two opposite AC waveforms.  When one is high, the other is low, and so on.  The voltage between them is 240 volts RMS; the voltage between either and neutral is 120 volts and used for simpler loads.
But many industrial/commercial buildings are actually fed with 3 phase power, as that is more suitable for industrial loads like large induction motors.  Instead of the 180 degree phasing of domestic power, industrial/commerical power is distributed at three equal points stepped 120 degrees around the phase circle.  Typically in such a setup, each phase to neutral measures 120 volts RMS, so simple single-phase outlets can be provided.  But since the phases only differ by 120 degrees instead of 180, if you measure the RMS voltage across any two (which is to say, measure the degree to which they are opposite) you'll only get a trigonometrically reduced 208 volts.  Install a domestic model electric cooker or clothes dryer at work, and it may be under-powered, though such simple resistive loads may not particularly care.
(There are also other 3-phase distributions schemes at higher voltage, &quot;wild leg&quot; etc - trying to keep this simple)