The only tank that I know of that is a Genesis style atty where a mesh wick can touch the bottom is the RSST and that's because the tank is only open at the top. It's like a bucket, so the wick can't physically touch the metal bottom due to the plastic. On all other Genesis styles the wick can't touch because it can potentially cause a short.
As for cotton only, yes - I use cotton in pretty much everything I build. Cotton yarn and cotton ball work even better if you just can't get the mesh to work. Sometimes it is hit or miss and honestly, I feel that the mesh sort of kills the throat hit. My cinnamon roll DIY juice rocks and has an awesome throat hit, except with mesh. If I drop the mesh and move back to cotton, it all comes back.
I like mesh, it works great when it works, but overall, I think cotton is the best option available on the market, if you don't try to dry burn it

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