the solution to the inbound capacity problem is simply to PAY for inbound capacity. off-chain mechanisms translate the cost of blockspace into the cost of provisioned capital. if you wanna save on L1 fees you'll have to pay for the workaround that lets you do that

this makes perfect sense for a strictly finite supply currency - you have to pay to have it served to you. if it's not credit, why would anybody else subsidise it for you?

because the money is finite, therefore each unit slowly gains more purchasing power, it makes sense to dedicate a percentage of it for the service - eventually the money pays for itself

no LSP frontend that I know of today (Phoenix, mutiny, breez, Zeus, etc...) is charging beyond setup fee, and so you cannot pay for a specific incoming capacity in advance, and it depends mostly on your first txn (which is weird as well) but I guess they all aim at the simplest ux at first

eventually future bitcoin users will understand that real bitcoin comes with a cost. the cost to transact on chain, and the cost to have the capacity to batch off-chain. freedom is not free