There are critical issues in Cross-chain centralised version of the ‘Lock & Mint’.
The easiest to implement cross-chain is the centralised version of the ‘Lock & Mint” where native tokens are given to a central custodian who in turn mints a synthetic version of the token on a target blockchain. The decentralised version requires the usage of decentralized custodians that are properly incentivised to behave appropriately. The majority of bridges, including those proposed by Cosmos and PolkaDot are of the ‘Lock & Mint’ variety.
There are still some critical issues including
1) Slow Speed
2) High Costs
3) High Complexity
4) The proliferation of synthetics of the same underlying asset