Removing 3rd party kernel access will probably also make cheating harder. Kernel anticheat is necessary largely in part due to cheat software using exploits in the 3rd party extension system to get kernel privileges itself and evade user mode anticheat.
I’ve been happy with Qwant lately, they have their own index so using them doesn’t support the Google + Bing hegemony. They’re also EU based and regulated by the gdpr.