Well yes, two different inflation rates and an ongoing ability to swap 1 ETH1 for 1 ETH2 is the issue, as far as I see it. I don’t see how a fixed peg would work in this situation and although you say it would work “Period” I don’t see how. What would you expect to happen the first day the beacon chain starts validating in this scenario?
I could see a floating exchange rate work (start at 1:1.2, for example, and move to 1:0.1 over time); if the change in the rate is known in advance it would allow market forces to move ETH1 over to ETH2 at the time they are comfortable with it (a later date would involve less risk but lower reward).
Eventually the exchange rate has to go to 0 or there be some mechanism in the deposit contract (or beacon chain) to stop accepting new deposits, as otherwise we could reach a state where the ETH1 chain is basically abandoned and someone can run it in their basement generating ETH1 and depositing them for ETH2.
(There are meta-constraints here, as well: we don’t want to see 100% of ETH1 being deposited in to ETH2 early on because then there will be no way of paying gas on ETH1, for example.)