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
のま【々】
(「々」が、かたかなの「ノ」と「マ」を組み合わせたように見えるところからの通称。「ノマ」とかたかなで表記する) 同じ漢字が続いて繰り返されるとき、第二字に代えて用いる記号で、読みは第一字に従う。漢字の「繰り返し記号」で、重字、畳字ともいい、かたかなの「ヽ」、ひらがなの「ゝ」とともに「おどり字」の一種。その形は「仝」の変形ともいわれるが、中国でも用いられていた二点
「
」
が日本で変化して出来たものか。同の字点。
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.