Two-way bridges between eth1 and eth2

If the “ETH2 as the finality gadget of ETH1” is enabled, favoring ETH2 over ETH1, how about putting Eth2Data in ETH1 block and adding a validity condition of ETH1 blocks (which is verified by ETH2 validators) that the Eth2Data must be a finalized block in ETH2 chain, instead of the Eth2Data voting inside ETH1?