Agreed with the above comments - most corals really only need light (and some nutrients), but some (typically LPS if I’m not mistaken; I might be, I haven’t looked into corals much yet at this point) do better with supplemental feeding. As bnord here points out though, water changes are pretty much ideal for smaller tanks, as you can pretty well keep parameters rock solid for cheap with little effort on pico tanks with them.
From the cost breakdowns I’ve seen, going the no water change route really only becomes cost effective on large tanks (like 100-150 gallons or more large, if I recall correctly), and maintaining good parameters in a pico without water changes would likely be substantially more difficult. Additionally, as Slocke mentioned, many soft corals in particular are known for basically engaging in chemical warfare (allelopathy) with each other, where they release certain chemicals (essentially toxins) to try and ensure they have room to grow and spread on the reef by trying to push other corals out. Water changes would dilute any chemicals in the water and theoretically prevent them from reaching really harmful levels. That’s not to try and dissuade you from attempting it or to say it can’t be done (after all, people do keep softies in no water change tanks without issues, though the tanks are usually much larger than a pico), it’s more just so you’re informed on what you’re getting into with that course of action.
So, with that in mind, out of curiosity, is there any particular reason why you don’t want to utilize water changes for your tank?
Also, just to comment about the majanos, the laughs came from the fact that most people consider majano anemones (no matter how pretty they may be - and some of them are incredibly pretty) to be pests, as they multiply relatively quickly and sting other things in the tank. If you like them, then you can certainly keep them and be proud of them, but be aware of the potential issues and the fact that most reef-keepers will find it very odd that you keep them (though a few would appreciate it, as there are at least a few people on here who have tanks specifically for cool “pests” like your majanos). If your tank does well, then you’ll probably need to remove some majanos on occasion to keep them from overrunning the tank/the corals, but that should be manageable in a pico without being overwhelming.
