Yep. Hosting any reasonably sized image will absolutely ruin you in gas costs.

They are put on IPFS which can exist forever.

URLs can also exist forever. The real point is that they are digital assets that don't exist on the blockchain itself.

The content at a URL can be changed at any time, NFTs that don’t prove that the content that serve hasn’t changed make for worthless NFTs.

IPFS is ideal for this use case because the URL contains a hash of the content meaning that either the original asset is served or nothing (which you can fix if you have the asset).

"can" being the operative word but is very very far from guaranteed. If you wake up one day to find that no IPFS nodes are pinning the content anymore, it is as good as gone.

Unless you or anyone else has a copy of the file, then they can put it back and the URL will be the same. If you own an NFT that points to something on IPFS you probably want to keep a copy of the file lying around to do this if necessary.

There are projects trying to create permanent decentralised, content addressable storage (in some case as layers on top of IPFS), so maybe even that problem will go away.

Filecoin attempts to solve that by adding an incentive layer on top of ipfs.