Let’s say miners really mine less and the difficulty drops, wouldn’t it weaken their competitive edge?
Why? The coin supply is finite, sooner or later we will reach the case, where the basic block reward will be zero. And then, users could fully decide, if they want to move their coins in a Proof of Work network, or if they want to get their transactions confirmed by Proof of Stake validators. Then, it may be pointless to mine zero satoshis on-chain by using Proof of Work. On-chain fees may be lower than off-chain Proof of Stake fees. What then?
or invest in Lightning's capacity
Lightning is similar to staking, but it lacks some features, like direct transfers between all Lightning participants. You still need to touch on-chain, you cannot send coins directly in Lightning, and finalize it later on-chain, you have to finalize that on-chain immediately, no matter what, because each channel should be in the right state to move any coins anywhere.
Unless your no-fork idea includes sidechains?
Well, sidechains at least have some independence, and only finalize things on-chain. But Lightning is fully pegged to the main chain, and that's why all problems from the main chain are always moved downwards to LN (for example, if on-chain fees are high, then there are problems with creating and closing channels).
"Good enough", how? If you have such difficulty it means there's very little work done. And if this internal-Proof-of-Stake system is dependent on Proof-of-Work, there's very little security.
If the basic block reward is zero, and on-chain fees are very low, then this low difficulty is justified. It just reflects on-chain rewards. And they will be lower if the whole system will move into LN, staking, or other layers.
How's block time relevant?
If you increase the block time from 10 minutes to 40 minutes, then without any fork, the difficulty will drop to the minimal value, and will stay there.
Here's a friendly suggestion: Let's talk about it. Don't implement theory if you haven't discussed it with others. There might be a "hole" you haven't thought of.
No agreement is needed, if there is no hard-fork, and no soft-fork needed. It is just about users willing to move coins as they want, and sign transactions as they want. They don't even need to move on-chain coins, they can create coins by signing something, then they will get their coins deposited on a separate chain. Later, they can move coins on-chain, then they will be destroyed on the sidechain. In this way, it is possible to create two-way-peg, where nobody can stop it. Then, it is possible to turn chains on and off, it depends only on users, they will have freedom they never had before. And the whole work is about making the right scripts, so that on-chain coins will move if (and only if) all participants will agree on that, and that will be needed only if someone will want to leave the sidechain.
make a paper, let us comprehend it
The basic idea is already shared, the original author thinks about utilizing it in the Proof of Work context, but I think it could be used as a Proof of Stake too. Many things are ongoing, because, as you can easily guess, Bitcoin community is mainly against staking, so to make it real, there is a need to allow the minority to use their coins as they want, and to gain and lose them, by testing their ideas in practice. If I would share my ideas in the current stage, they would be destroyed by the Proof of Work community. They should be hardened, and more work is needed to make some unstoppable proposal, but the main idea of unstoppable sidechains (without any fork) is very promising.