Trying to get ultra pure water for your fish is a noble gesture, but it ain't gonna happen...
If all you do is replace evaporation with RO or distilled water, you will be diluting TDS and other factors contributing to hardness. The processes of distillation and reverse osmosis remove nearly all hardness/TDS. So if you started with something like 20ppm of hardness, then let water evaporate, you might get up to 25ppm. Then you add the distilled or RO water, you have diluted it back to the original 20ppm. Actually, over time you would see in increase (not even counting outside factors) because if you check an RO unit with an electronic TDS meter you will not find a reading of zero. There will be more and more as it comes time to change the filters in the RO.
The main thing we are concerned with in doing water changes, really, is keeping Nitrate under control. If all you are doing is adding to make up for evaporation, you're not just spinning your wheels, you're losing ground. Two things are increasing the Nitrate concentration in your tank. One is evaporation - Nitrates don't evaporate with the water, and of course, your fish are still producing ammonia, which becomes Nitrate.
Reverse Osmosis cannot be relied upon 100% to remove biological contaminants. Neither can boiling. There are heat resistant strains of bacteria that can withstand temperatures well above 100C. The only way to heat water above that temp is under pressure, like in a pressure cooker, or an autoclave. The catch is, as soon as the water comes in contact with air, all bets are off.
Unless there are problems with the water, don't worry about softening it. That hardness can be a good thing. With no hardness, there is no buffering capability, and you could have serious pH problems.