Tracking Bitcoin Block headers in Tezos Blockchain

Hello everyone,

I do not know if this has been discussed before, but would love to get your view on this:
What if Tezos Blockchain tracks Bitcoin block headers. Considering block header is just 80 bytes of data every 10 minutes, it is not a lot of data to add to Tezos blockchain.

This can enable cool things-

  1. Trustless swap between Tezos and Bitcoin(using HTLC).
  2. Trustless minting of tzbtc in Tezos Blockchain. Claiming back BTC on the Bitcoin blockchain still needs to go through a trusted third party(but may be trustless swaps above could be used instead).
  3. If Schnorr aggregate signatures(will soon be supported on Bitcoin) could also be supported on Tezos, enables two way transfer of Bitcoin between Tezos and Bitcoin blockchain.
  4. It’s a big win for both Tezos and Bitcoin.

We can develop this as a Smart Contract, no doubt- but it would be a lot of data to populate those 600,000 block headers costing a lot of fees. But if the first 600,000 block headers was bundled along with a protocol change, adding new block headers could be managed by the bakers(just like the harbinger protocol- for getting price feeds).

What are your thoughts on this?