Bitcoin should switch to BFT (Byzantine Fault Tolerant) PoS which is secure by definition. Most people that don't like PoS are thinking in "vanilla" or "chain based" PoS protocols which are certainly more insecure than PoW.
Ethereum 2.0 is using Casper currently in the Beacon Chain, and other coins are also using BFT PoS protocols. I will ...
It's a complex question because you can never just consider scalability on its own. Something to keep in mind when talking about scalability is Vitalik's infamous scalability trilema.
The trilema involves Scalability, decentralization, and security.
It states that increasing one always sacrifices something in regards to one or two of the other components.
No, the concerns limiting the number of transactions are orthogonal to the method of achieving consensus.
Blockspace is limited to prevent the cost of operating a node from ballooning to enable users to perform full validation. Neither the effort for PoS nor PoW scale with the number of transactions in any way.
Is this the correct way to calculate security for bitcoin proof of work?
Not sure. But looks like lot of things are ignored in these numbers. I have read about FRM so I will share few things related to FRM ratio and security:
The Fee Ratio Multiple (FRM) is defined as the ratio between the total miner revenue (blocks rewards + transaction fees) and ...
In addition to other answers, Bitcoin investors would also like to have a very conservative approach to updating bitcoin. Messing with the core idea will increase the perceived risk for something wanting to be a store of value.