Surely, from our perspective an expanding universe would look exactly the same as a universe in which everything is shrinking away from everything else?
This is false. If everything was shrinking away from everything else, that would imply that the recessional rate of distance we observe due to this shrinkage would be independent of distances. Afterall, all galaxies are shrinking at the same rate so the rate they "recede" is only dependent upon their shrinkage rate.
However, we observer that the more distant an object is, the faster it recedes from us. This is the premise of Hubble's law and is only explained if we assume the universe is expanding.
Furthermore, there are many objects in our visible universe which are receding from us faster than the speed of light. This is only possible because these objects are not moving through space, but rather space itself is expanding. In your scenario, these objects are shrinking in space (I presume) and there's no possible way they could shrink fast enough to appear to be receding faster than the speed of light.
"Oh, but the red shift!" I hear people exclaim. Well how about this:
The speed of light is simply slowing down.
There have been people who have tried to suggest that the universal constants (e.g., the speed of light, the mass of an electron, etc.) are not actually constant and instead time-varying (albeit slowly). No such theory has ever been successful.
Again though, your idea suffers from a few problems, even if you assume it to be true. There are multiple kinds of redshift. Redshift from receding objects occurs because space itself is expanding and causing the wavelengths to expand as a result - otherwise known as cosmological redshift. In your scenario, the redshift would be caused by the (faster-than-light) recession itself (since the galaxies are physically moving away from us), also known as doppler redshift. You then complicate the problem by making the value of the speed of light change over time. This would cause light, at the moment of emission, to be redshifted both by the doppler effect and by the slowing of $c$. As the light travelled, the time-varying of $c$ would have no effect on the wavelength. In this scenario we would have long ago realized that moving objects get a double redshift, namely the doppler effect and the time-varying $c$ effect. We just don't see that.
If the speed of light is a measuring stick against which all things are measured, and if the speed of light is slowing down, then it means everything shrinks
Those two ideas don't relate at all. There's nothing suggesting the speed of light slowing down implies everything shrinks.
high frequency waves generated in the past are observed with a lower frequency today
As explained above, your proposal would cause the redshift to occur at the time of transmission, not en route. So there wouldn't be "high frequency waves generated in the past" They would have been emitted as a lower frequency. Which itself is troubling because how then do you explain the CMB changing frequency over time?
What is wrong with my alternative?
Aside from the above mentioned points, a huge number of things:
- All the physical constants of nature are tied together. You can't just change one and hope that the others don't notice. If the speed of light is constantly decreasing that has drastic implications throughout all of physics. For example, if the speed of light changes, suddenly the electromagnetic force strength changes, atoms aren't stable, and the universe explodes! What is your proposal for stopping that occurrence?
- Just how exactly are things shrinking? Are the atoms getting closing together? Are the atoms themselves shrinking? At some point you're going to hit a limit and your object becomes a black hole. Are you really predicting that eventually the universe will be nothing but black holes? My guess is that if you did such a calculation, you'd find the time it took to reach that point is about a second, but the Universe has been around for a few billion years.
- What caused this initial shrinkage? Motion requires energy input. Where did this energy come from? How did it apply itself so uniquely as to cause every individual thing to shrink into itself and only itself?
- How did the universe get to be so distributed? Your proposal basically implies the Big Bang didn't happen since you attempt to explain things the Big Bang theory already explains. If your explanation differs and you believe yours is the correct one, then the Big Bang Theory cannot be correct. If that is the case, then how did the universe get into its current state if not the Big Bang?
I'm sure I could go on and on, but hopefully you can see there are more than a few holes in your idea. No offense, but it takes years and years of studying to contribute to the forefronts of science. Ground-breaking ideas aren't going to be had by someone who read about a few concepts from Wikipedia or A Brief History of Time and decided they could come up with a better theory. That's the academic equivalent to reading about the rules of (American) football and deciding you can play in the NFL.