More computationally intensive, yes- but computationally intensive may mean "running on smartphones in the background for .1% reduction in battery time" or "a medium-sized country".

Increased cost is certainly not so straightforward. If you're sufficiently distributed, using already-existing hardware, with spare compute on extremely efficient devices, it could conceivably cost less. Even if a centralized server farm would be doing an order of magnitude less math, smaller processors use an order of magnitude less power to do that math.

Bitcoin proper has a central ledger- every miner needs to hear about your transaction to verify it. Lightning is a clumsy way of reducing how many actors need to be notified of your transaction. Better currencies include stuff like that as first class. It's all in the name of getting closer to a constant-number verification scheme that is closer to competitive with the O(1) of registering a transaction with a bank.

Centralized credit/debit cards exist so that a big wealthy firm can say yes, this person has enough money for this transaction and I will guarantee the transaction by paying for it even if they can't. What I would really like to see is distributed, automatic guarantees: when you buy something at a coffee shop, people running validators on wifi will pick it up and use their staked currency as insurance (hedged by the system) that they know accounts who trust this particular account, and the transaction is valid. More people staking and trusting this account means more trust by the larger system, which then only has to validate aggregated transactions. Anyone announcing themselves at a validator plugs in at a given level of aggregation, all of which have different staking/network/latency/storage requirements. Unlike off-chain transactions (eg lightning), the system is guaranteed at every level.

Any given transaction will still be validated dozens or hundreds of times. En bloc it will probably use tens or hundreds of times more energy than the server farms powering VISA. I'll be honest, I'm okay with that. I really like the idea of having a bank account that isn't tied to a company.