>transaction fees will prop miners up (though it hasn't happened yet so it's valid to be doubtful this'll happen in practice)
No, they won't. This is a common talking point, but it is rarely accompanied by facts. Consider that fees currently amount to about about a percent of the total miner payout. There is some research that indicates that bitcoin is vulnerable to a class of double-spending attacks known as selfish mining:
https://eprint.iacr.org/2020/094.pdf
http://fc14.ifca.ai/papers/fc14_submission_82.pdf
>And also depends what you mean by securing. All clients, miners and not, are capable of checking transaction and discarding "insecure" and invalid chains. I don't need a miner to tell me if your transaction is valid or not.
No they aren't. You misunderstand the fundamental design of bitcoin. The problem is not that the non-mining nodes cannot verify signatures or something, the problem is that these non-mining nodes will not be able prove to each other that the signatures to not refer to already spent funds. The non-mining nodes cannot conclusively prevent reorgs that can be used for double-spend attacks.
>All clients, miners and not, are capable of checking transaction and discarding "insecure" and invalid chains.
They do this by selecting the chain with the highest amount of PoW associated with it. If the network hashrate is low relative to an attacker, then any attacker will be able to easily overpower the network and decide which chains are invalid.
If you are new, I recommend this video on bitcoin's design: https://www.youtube.com/watch?v=bBC-nXj3Ng4