It would create a confusion, the miner will have two options either to proceed the token or transaction with highest fees.

If it was the miner who want to do that, it's up to them, like viabtc who offer free transactions priority.

I don't think this is a good idea, people will adapt based on the environment. If the usage of Bitcoin as a currency is very high, people would find a way to spend Bitcoin cheaper which is using LN, for now Bitcoin is rarely used as a currency, hence people stay to use on-chain.