Well the current theory of cosmic expansion does exactly that. The cosmological red shift is thought to be due to spacetime expanding and thus stretching the waves out over time, which makes them redder because with a longer wavelength the frequency goes down. Similarly the Cosmic Background Radiation, which pervades the universe in all directions, is the same as that given off by a body with a temperature of just under 3K. This is thought to have been originally emitted by a very early universe that was hot enough to glow, but because the expansion has stretched the radiation so much since, the effective temperature of the radiation has gone right down to a value close to absolute zero. The universe seems to be still expanding, so light presumably continues to be stretched over time. Not that the effect is one we can see over human timescales, though.
One potential conceptual problem is connected to the concept of space-time and energy. The doppler shift is connected to distance; wavelength changes due to motion and velocity. However, within energy or photons, frequency; time, is the dynamic variable, and distance is the passive variable. We can measure distance with a meter stick which is a passive measuring device. Time needs a clock which needs energy; a dynamic tool is needed to measure the dynamic variable.
The red shift takes potential energy away from the photons; red defines less energy per photon than blue. Since time is the dynamic variable, that needs energy to be measured, a time shift should be leading any changes in photon energy, with the wavelength passively adjusting.
As a simple example of a time modulated doppler shift, say we have a train that first approaches us, then passes by us, and then moves away. We will hear the pitch of the train's whistle get higher; approaching, and then start to lower, after it passes us and moves away.
Picture this scenario. The train is stationary. We put on a blindfold. The engineer tweaks the pitch of his stationary whistle, so it sound like the train is approaching and then the train is moving away. The frequency tweak of the whistle can give us the same measured wavelength affect as motion, since the wavelength will change if we adjust the frequency. Light can be tweaked in both ways.
The moving train scenario, differs from the universe, in that the train stays within a single non changing space-time reference frame. The expanding universe, is changing the universal space-time reference frame continuously; expanding, with potential energy going into mass as gravitational potential. There appears to be a dynamic energy exchange going on that leads to less photon energy; red shift.
This suggest that there is a time tweak; exchange of the conserved energy in the photons. The expanding universe, by increasing complexity, as space-time expands, suggests universal entropy is increasing, which is endothermic.
Time has more in common with entropy than it does energy. Time moves in one direction; future. We do not get old and then get younger in cycles. We are born, age and die; one direction. Energy cycles like a wave and thereby repeats itself over time. The natural path for entropy is linear and always increases to the future; 2nd law is connected to the unidirectional flow of time.
Entropy times temperature has the units of energy; free energy. My guess is the flow of time, as space-time expands, leads to frequency modulation, mediated through entropy increase. This entropy changers times the background temperature T=3K, becomes the vehicle by which energy is traded.