Conversation

On-chain transactions are only usable as a settlement layer. The fee for sending 1000 BTC is the same as 1 BTC if both were a single UTXO. The arbitrary limits on block size and time don't accommodate doing on-chain transactions for absolutely everything. Have to use 2nd layers.
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Nothing prevents making Bitcoin support 1000x as many transactions by having 10x faster block time and 100x larger blocks. It isn't a viable way to scale it up to support every little transaction though. Resource use for mining isn't directly related to transaction throughput.
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If it supported 1000x as many transactions, it would need 1000x more storage space, so it would be much harder to run a node. There would be more space, so more transactions, but lower fees. Miners would end up getting near zero money from fees until it filled up to 100% again.
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Even if you can throw away the old history, there's still the issue of bandwidth, latency, etc. It's less common now, but some miners used to produce empty blocks with no transactions simply to get the block rewards due to fees not being a substantial portion of the revenue.
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They're only hashing the header, so it may seem strange that they'd throw away the money from the fees. Some of the miners in China were apparently having issues fully syncing with the network due to the Great Firewall, etc. so they'd just make empty blocks instead...
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Note: nodes are still validating even without mining. The mining security isn't needed for the basic transaction validation, etc. It's needed because the valid history path is the one with the longest chain of blocks. It's the consensus mechanism for which block(s) are canonical.
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If there are only enough fees to support 1/100 as much mining as today, Bitcoin still happily goes onwards with 1/100 of the security against replacing the history with an alternate, still valid history. Non-mining nodes including those wallets use, etc. still validate.
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Mining hardware gets more efficient, electricity will get cheaper, etc. so hash rate can still go up with essentially less mining happening. If you can mine with lower costs, you displace the miners with higher costs. Limited pool of revenue to split and you start losing money.
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