Going to build a trust minimized bridge between ETH and ETC

I believe that decentralized technologies in a sense are fundamentally monopolistic, or how do I word it even. The biggest network is always the most secure, being used more and more, attracts more and more capital with time. Besides the lesser are the fees on ETH, the more trading algorithms become profitable, therefore miners will not lose incentives to secure the network. So I fail to recognize inhabiting ETC as a threat to ETH security. ETC will always remain a smaller network. Stop me with an argument.