The tx’s get broadcast eventually but ideally there’s rarely need to close a channel at all and most users won’t be running their own node anyway so they won’t have to deal with the base layer at all.

Bitcoin is “slow” by design. Lightning fixes the variable time and cost it takes to send a transaction. All the other “faster” blockchains all make trade offs in terms of decentralization and security and they all have some sort of governing entity. Oh, and don’t get me started on PoS.