Assuming you control your device (non-corporate non-government users) and know how to configure your DNS server (elite users only) and wanted to do this extra step (privacy-conscious people?), this will break for hotels, airports, cafes/restaurants, corporate/government networks, anyone with an ISP that intercepts public DNS requests, and various home routers. Not to mention making surfing the web much slower and less reliable, since we distribute name servers specifically to rely on caching to lower latency and increase availability in case of various network failures.

But otherwise, sure, that works.