I only use self watering pots for plants that don't like to dry out. In fact, the only way I have been able to get ferns to survive is to have them in self watering pots. Currently, I have a maidenhair fern and an alocasia polly plant in self watering pots and they are doing great. Make sure you get self watering pots that have a reservoir and wick; I find that these keep the soil more consistently moist. Absolutely do not put succulents or cactus in self-watering pots.

Plants that get dramatic between waterings work well with self watering pots. I have my fittonia in them and there's a big difference between them and normal pots. I would suggest them for plants that don't like fully drying out between waterings.

I’m a big fan of using them for growing stuff semi-hydroponically.

https://www.lecaaddict.com/leca-information/why-grow-in-leca

I have balcony plants in them - petunias, basil, some outdoor begonias, chives.

I think they’re convenient for hanging plants, but with most of my plants I’m more concerned about overwatering than underwatering so they’re not ideal.

My calathea is the only plant I’d say truly thrives in a self-watering pot. I have a few others in self-watering pots- philodendrons, alocasias, aglaonemas- that are varying levels of ambivalent about their pots. I need to be careful not to leave them too wet and will likely be repotting them into normal draining pots.

Personally I just treat them like regular pots. I have a handful of plastic hanging ones. mostly because I couldn’t find anything else that did what I needed for a reasonable price. I’ve got syngonium in mine.

I don't understand the issues surrounding bottom watering pots with a wick.

I have a number of succulents in them, and of course the usual unkillable Pothos. I partially/fully fill the bottom part (Depending on it's carrying capacity) once every 2+ weeks and for the succulents they're good to go. Saves me A LOT of effort doing the usual bottom watering process of putting the pots in a large container of water until the water saturates the soil.

Can someone go into detail on the downsides of such pots?

I had success with a marble queen pothos. Right after I re-potted it in the self-watering pot, it had a big growth spurt and doubled in size over the last 3 months. Used a soil mixture with mostly perlite, which may have helped aerate the soil without needing to let it dry out.

I have only killed plants in self watering pots (with soil). Semi hydroponic is the way in these pots as far as I'm concerned. Pothos worked pretty good for me.