> It still seems like a valid metric, you just need to multiply the number of bitcoin transactions with some factor for the average number of outputs
Nah. You don't need to double and triple down on wrong ideas and metrics that are scientifically spurious. You know calculus so you know multiplying by averages won't tell you what you want to know.
Transaction count relative to energy usage doesn't tell you what's valuable about the observed system and its energy consumption, which is its decentralisation, censorship resistance, assurances, and trustlessness.
Assuming you care about logic, simply update your broken mental model.
Because batching will increase as Bitcoin grows, and has practically infinite throughput, its efficiency improves exponentially by securing more value relative to energy consumption.To secure ever more value using the Bitcoin network, humans are incentivised to find and build more efficient energy sources.
Further, an arbitrary number of transactions can occur securely offchain and get aggregated and finalised on-chain i.e the settlement layer. In fact this is how the future will be. See Lightning, Liquid, other L2 designs. The order of operations is first to have a bulletproof settlement layer.
Bitcoin was designed to be the single planetary currency. Spend time studying it and you'll realise that Satoshi was smarter than all his current critics who all imagine they've brilliantly and uniquely perceived some fatal flaw in Bitcoin's engineering, game theory or economics.
Remember, if Bitcoin were a company, it would currently have a market cap of >USD800B. Few programmers can build anything that valuable let alone critique it meaningfully.
Let go of useless, poorly reasoned concepts.
Humble yourself and study Bitcoin. It's a wonderful optimistic scientific discovery on par with fire, antibiotics, and electricity. http://lopp.net/bitcoin-information.html