I wouldn't necessarily say 々 is used to avoid having to write the same kanji again, but rather to make it clear that the word is obtained by duplication of a character — moreover the reading should be doubled (with rendaku where applicable).
For example, 日本国語大辞典 (via kotobank.jp) has
日本国語大辞典 via kotobank.jp, emphasis added
Whether you take it as a hard rule or not, I don't think anyone would think it a good idea to use 々 when then reading of the kanji is different.
For example, one usually writes
In principle both can also be written 日日 (which they usually aren't for disambiguation), but I don't think that 日々 would ever be used to mean 日にち.
Just for fun, there is of course 明々後日 shiasatte, but this is probably not what you had in mind.