This is generally intended to help speed up the delivery of data from content delivery networks (CDNs), by allowing better use of DNS-based load balancing to select a service address near the client when the client computer is not necessarily near the recursive resolver.
[1][2] When an authoritative name server receives a DNS query, it takes advantage of ECS DNS extension to resolve the hostname to a CDN which is geolocationally near to the client IP's subnet, hence the client makes further requests to a nearby CDN, thereby reducing latency.
Because ECS provides client network information to the upstream authoritative DNS server, the extension reveals some information about the client's location that the authoritative DNS server would not otherwise be able to deduce.
[4] The owner of the site believes 1.1.1.1 too often routes recursive DNS requests in a non-geographically-optimal way, causing poorer connectivity than if the feature was available at all times.
[4] Cloudflare CEO Matthew Prince cited privacy concerns as reason for 1.1.1.1 to not support ECS.