Significance of signal energy in audio?
It seems to me that the energy carried by a sound wave should be
  proportional to frequency squared.


Why? What makes you think that this is the case ?


  But in DSP they are all considered to have the same signal energy
  (integral of x(t) squared)


The concept of associating power or energy with a a digital signal is somewhat tricky. Digital signals are just a bunch of numbers so assigning actual physical properties to them doesn't really work unless you carefully define the context. 

Mostly the concept is used assuming that the digital signal is an accurate representation of an analog signal that has actual physical properties. If this relationship is well defined and constant you can compare the sum-of-squares of two different digital signals and draw some conclusions on the energy difference of the actual analog situations. However, that really requires "all things being equal" and there are actually a lot of things that need to be equal for this to hold.

STEP 1: basic physics of power

Power, intensity or energy are typically defined or calculated as the product of two field quantities (not one). In electricity power is defined as the product of of voltage and current. Simple example: if your signals were defined as "voltage over a one Ohm resistor", than you can indeed calculate the power by summing the squares and it would be the same power for all of your three examples since the current is proportional to the voltage. 

If it were the voltage over an ideal inductor or capacitor then the answer would be wrong. Average power over one of these would be zero in all cases. For an ideal inductor voltage and current are 90 degrees out of phase and the average power is therefore zero.

STEP 2: physics of sound

The two field quantities that make up a sound wave are sound pressure and particle velocity. First you need to define which one your digital signal actually represents. Most of the time it's pressure but many second order microphones (cardioid, dipoles) will create a signal that's proportional to the particle velocity. If you are far enough away from the sound source than pressure and velocity are in-phase and proportional to each other and the proportionality factor is the free field impedance of air (density times speed of sound). In this case you can actually calculate the intensity at the microphone position by simply squaring and scaling. If you are close to a sound source that doesn't work anymore and you actually need to measure  both signals.

As others have said: per it's physical definition sound can't exist at 0 Hz. Sound pressure is a variation of pressure around a steady-state average and if there is no variation there is no sound. 

Step 3: human perception

Sound energy and perceived loudness are only loosely related. Human perception is very dependent on frequency and its quite non-linear. Building good loudness models is quite difficult. Simple example: 1 Watt of sound at 1kHz radiated into a typical residential room would extremely loud and quite painful. At 50 kHz it would be utterly inaudible, even though it's the exact same amount of physical sound power.