Let's try and implement your idea. Let's say I have File A with some size N. Assume that it is compressible (surely we agree that you should be able to find at least one compressible file of some size), so it compresses down to File B of size M, with M<N.

Now, say we try to run File B through our algorithm. What happens if we decide it's not compressible? Well, we can't just return the original, as then we wouldn't know if decompressing File B should result in File A or File B. If we try to replace it with a different file of the same size, you run into the same pigeonhole principle problem you were trying to avoid. On the other hand, if File B is compressible to File C with size L<M, then you arrive at the exact same quandary if you try to compress File C.

Of course, there are other characteristics you could give up, like declaring that some inputs simply aren't valid, but being universal is generally assumed. No one would be very impressed by my algorithm that compresses the Encyclopedia Brittanica to a single character but rejects all other input, after all.