Most users will want to own NFTs, use them, enjoy and sell to make money, or forget about them. Most NFTs will probably have short lifetime of hype and then go to oblivion. Some very rare ones will have longer life time.
If I were a typical consumer or gamer I would probably be too scared, lazy, and disinclined to move my NFT anywhere, except if I can make lots of money buy selling it.
To sell an NFT you can perfectly stay on the platform where it is stored. So again there is no point moving it.
A place like OpenSea can perfectly make many chains look like the same market place. You can perfectly buy an NFT on its native chain, transfer it, burn it, whatever.
So my subjective prediction is that people will move liquidity to NFTs and not NFTs to liquidity. When you buy a house, theoretically you could disassemble and move it to a different place. Very few people do it though. Very much same for NFTs. There is simply no strong purpose to overcome general human laziness. Theoreticaly, you can export and move your data from FB to Google to Instagram whatever. In reality I have never met a single person who did it. Same for NFTs.
It is interesting to create solutions that potentially move NFTs but they may be beyond the need or comprehension of a typical consumer. Security problems will multiply incredibly and probably unsolvably if an NFT is moved around different incompatible platforms. Add to this that for most of these platforms there is zero information on how they actually work and a number of security problems that people that runs these platforms simply hide.
The only thing that will be moved in large quantities between chains is money and this will be done by professionals (liquidity providers, money makers, etc)
Subjectively, if I ever own an NFT, I will keep it where it is.
So in my view, moving NFTs is a solution in a search of a problem. What will probably happen in real world, is that DeFi apps will have replicas on each chain, and if you want to use your NFT in defi, you will use it on corresponding replica. People that provide liquidity for DeFi will move it in big chunks to different chains. This is very much what is happening now already.
So moves will be done by professionals only. The unavoidable complexity of the move will be compensated by return on liquidity. Consumers will probably almost never need to move anything anywhere.