doesn't that solve one of the problems with bitcoin which is a decentralized way to store bitcoin core?
Of course not. Storing a binary alone will not make it decentralized. If someone will upload Windows 10 ISO on-chain, does it mean Windows will be decentralized?
no but who said anything about storing a binary. i was talking about the source code. that makes it decentralized. when you can store the source code on some place like the blockchain where a third party doesn't have the ability to remove your account.
I would propose usage of IPFS or BitTorrent protocol instead. If Bitcoin Core software remain popular in future, you can find peer who store such data even after many years it's created.
it's not free to make an inscription. they do have to pay
Only if that transaction is broadcasted in P2P way to other nodes. In case of almost 4 MB transaction that started Ordinals, it was mined by Luxor. One pool with sufficient hashrate is enough to make the chain bigger. Attackers could reach 1% of the hashrate, and then they can put a lot of inscriptions for free every 100 blocks.
It's only free when there aren't enough unconfirmed transaction on mempool to fully fill the block. Otherwise, the attacker actually trade transaction fees with storing their own TX/data. And in past few months, blocks is almost always full (in terms of weight unit).