Now if there could be an open application layer built on top of LN that including NFT funtionality (have no idea if this is even possible), rather than having to go with one of these sidechains controlled by companies which is pretty much no different than altcoins, I think that could have a possibility of being something big on Bitcoin.
That's exactly my thought / question: Is this even possible? When It's possible why is there nothing like that or am I not searching enough?Building a NFT Game with BTC. Where Do I even start?
Start with an explorer/marketplace for Bitcoin NFTs 
But not using a sidechain.I haven't yet read up enough on NFTs to confidently answer your question, but I'm pretty sure that they work a bit different from what you described.
Also, I already came across 'Bitcoin NFTs', which are sold on https://raretoshi.com/. While it's 'on BTC', it actually uses the Liquid sidechain.
Also, I already came across 'Bitcoin NFTs', which are sold on https://raretoshi.com/. While it's 'on BTC', it actually uses the Liquid sidechain.