This is an interesting problem to say the least, while allowing other chains does lead to increased revenue for the DAO, it also may lead to declining EVM dominance. In my opinion it is not possible to restrict development of technology on any chain, even if we decided not to allow other chains to fork arbitrum codebase, the builder will just choose another solution and go about their deployment.
Hence I think that the DAO should consider allowing other chains to use the Arbitrum codebase and perhaps we can increase the fees by a few bps for deployment on other chains to still incentivitze folks to build on Ethereum, but also capitalising on the fact that the technology which is in demand can be leveraged to fuel the Arbitrum DAO.
Is there any solution to permissionlessly bridge fees back to Arbitrum DAO instead of collecting the fees in a multi-sig?