SPV isn't for checking the honesty and integrity of the entire blockchain, it's only useful to confirm if YOUR payment was included in a block.

You are trying to have it both ways, on one hand LN wallets are trusting third parties too much and on the other hand you think we should trust the miners more.

What you are missing is that if there is a fork due to miner collusion, and nobody realizes it because only a miner would bother holding the entire blockchain and people are only using SPV with their light wallets, then there is possible all kinds of mischief like arbitrarily changing the miner block reward.

Here is the key: If it's the wallets that hold the verification power, then it's the wallet holders that have the choice of which fork to spend their coins to and therefore which chain the transactions will be submitted to. The "proof of stake" in every HODLer's wallet are what holds the hashpower providers hostage to stay honest.