Isn't that worse though since your data would be spread across multiple potentially untrustworthy parties instead of just a single one? Given how many requests a browser makes and normal browsing habits like regularly visiting the same sites, it would eventually lead to each resolver having a full profile of what you browse.
That makes me think of the reason Tor has Entry Guards where the first hop is limited to just a few selected nodes instead of random: https://support.torproject.org/about/entry-guards/