> So in theory, it's possible to just trade bitcoins off-chain (either on another blockchain or just using boring centralized tech) without necessarily incurring a corresponding increase in mining-related costs, right?

The mining-related costs are mostly unrelated to whether the bitcoins are traded on-chain or off-chain. The mining-related costs are more directly related to the price of bitcoin, or rather, how much a miner can earn with the block rewards and transaction fees. By trading bitcoin, even off-chain, you increase the demand for bitcoin, and therefore indirectly increase its price; the only difference is that by trading off-chain, the miners don't receive the transaction fees (which are currently less than 2% of the block rewards).

But if you’re trading bitcoins “off-chain”, doesn’t that mean you’re negating the point of a blockchain-based currency?

Yes, but for my purposes as a layperson using a currency, I'm choosing to trust a system that is opaque to me anyways (be it a bank/exchange/other financial institution vs a validator pool). One could argue, for example, that anti-fraud mechanisms in off-chain systems don't have a on-chain counterpart, despite being a desirable feature, so IMHO, if the argument goes that crypto can't do things on-chain that regular currencies can, it seems most feasible to just treat them as digital assets to be tradeable over existing centralized systems, no?