If you control parts of the plaintext, a well-designed cipher doesn't tell you anything about the rest of the plaintext.
But if you control parts of the plaintext, a compression algorithm will absolutely tell you information about the rest of the plaintext. That's its job—identifying similarities between different parts of the plaintext.
And it will leak that information in the form of the size of its output, and the standard definition of "well-designed cipher" doesn't do anything to mask sizes; the size of the encrypted data is the same as the size of the data passed to the cipher. So now both the data and its size are sensitive, and nobody's encrypting the size.
(You could sort of work around this by padding, but then you've basically removed the point of compression.)