Are basic replacement ciphers always bad for structured data encryption? I have read that basic replacement ciphers, such as replacing one byte with another specific byte at each location, are far less effective with non-randomized data. My question is, can this problem be mitigated to the point where basic ciphers can be effective on structured data by encrypting the data with other methods before passing it through the basic cipher?
For encrypting exclusively highly structured data, are basic substitution ciphers useful from early on in the encryption process, such as directly after something simple like a single XOR, or only after heavy encryption or should such basic replacements be avoided for this purpose all together?
A good encryption should produce data that are indistinguishable from a random stream. If you simply replace bytes with other bytes, and each byte has always the same replacement, many statistical characteristics of the original message remain. For instance, if the original message is text, then the frequency of each letter will remain also after applying byte-by-byte replacement.

by encrypting the data with other methods before passing it through
the basic cipher

If you encrypt the data with other methods, for instance with AES, there is no need to do any further encryption of the encrypted message. AES is unbreakable.
The question about multiple encryption was answered on SE many times. See for instance this.