Liquidity premium isn't relevant here. The concept of the liquidity premium explains the differences in prices of otherwise identical securities as a function of their liquidity. What you're thinking of is called slippage, the difference between your target price and realized price for a trade.
When running an ETF arbitrage strategy, your concern is not explaining the price of the relevant securities. However, you do care whether you can enter and exit positions profitably. Slippage models are highly nontrivial.
> ETFs that trade illiquid assets should simply trade at a discount relative to their "last traded price" NAV
Many closed ended funds do in fact trade at a discount to their NAV.