It seems that FreeDV encodes the input audio signal in both the frequency and time domains, which means that the output signal amplitude doesn't follow the input signal amplitude, but rather the output level from FreeDV is always high, even with no input audio.
Nah, that's not really the case. FreeDV uses a multicarrier scheme with 14 orthogonal carriers. Each of these carriers a (differential) PSK signal – i.e. one with constant envelope. Math (to be specific, the Central Limit Theorem) says that if you add up "many" independent, but identically distributed random variables (combining the 14 carriers into one signal), you end up with a (approximately) Gaussian distribution.
And that is good. It means we get the most information across, given a fixed output power. Any other amplitude distribution is worse (for the continuous-amplitude case, at least; see: Differential Entropy).
More info with same amplitude means we have, within the same bandwidth, more "room" to make our transmission robust. That's one of the reasons why FreeDV under low-SNR scenarios is usually better than analog SSB.
This is a real problem for some SSB transmitters and amplifiers which are designed to not operate at constant 100 % output, and the continuous high output can cause them to overheat.
These things will overheat because of the power put through them. So, we can find a power that they can continuous work with, and just work with that.
In other words:
Scale down your amplitude.
Also the continuous 100 % output causes batteries in portable SSB equipment to go flat much quicker.
Whether you transmit an average of 1W of SSB AM audio or 1W of FreeDV digital data should make little to no difference to the amplifier current consumption. Notice that you'll need higher peak power to reach an average SSB power of 1W, because FreeDV is more evenly distributing the power.
In other words: by using a mode that has a more constant power, you're making the most of your amplifier. The other mode is the one "wasting" power – it's only transmitting at full power when you make a very loud sound!
Is there any way to make FreeDV encode the input audio signal only in the frequency domain so that the input signal level is preserved ie: no audio input produces no output from FreeDV ?
No, and that would be highly undesirable, because it would negate the positive aspects!
So, you're misinterpreting an advantage as a misadvantage; FreeDV makes use of the power you have. Of course, you're totally free to just reduce the output you feed into your modulator (simply scale it with a factor < 1), and thus reduce the output power of your amp. That will still be more reliable than a full-power AM SSB transmission.