It’s just simply a fuel problem. As you pointed out, all energy comes from those dilithium crystals. There are other sources of energy one could harness but it won’t be remotely enough to power the ships systems. The replicator specifically uses a MASSIVE amount of energy and the conversion from matter -> energy -> matter isn’t a 1:1:1 ratio. There’s loss. So you’re always going to require some sort of fuel source which is the crystals.
However dilithium isn’t common to start with but surface-level dilithium that doesn’t require intensive mining operations is rarer still. The rationing gives Voyager more time and more dilithium for all primary ship functions. The ship likely wasn’t fully stocked with all needed dilithium for the trip because honestly it didn’t need that much for the initial trip it was taking. Once getting into the Delta quadrant they needed to stockpile in the event of coming into contact with hostile entities for an extended period of time, see ‘Year of Hell’ as an example of that.