On-chain transactions also happen when closing the channel; thats how final balances are settled on-chain.
You ask an excellent question about simulations. I would appreciate more information about that, myself.
Im asking mostly because Peter Rizun and Andrew Stone claimed on (I think it was) Scaling Bitcoin 2017, that they had simulations of bitcoin working with 1GB, or even 1TB blocksizes, and I was curious about what and how these "simulations" were being done and how legit are those.
https://www.youtube.com/watch?v=5SJm2ep3X_MIf they can do simulations to test how the system behaves at a certain scale, I guess simulations with LN could somehow be done.
Also, I remember hearing about how you could make money by having an open channel with a certain amount of BTC (kind of PoS for BTC through LN). What are the details on this? (I guess it's the fee that you mentioned), how would the profit that you could make depending on your stake be calculated? and what are the implications of this game theory wise.