So does chrome (and android webview which is now based on chrome) on lollipop and above. Where did you get the idea that it wasn't? Go to chrome://inspect on your desktop, you need to have a Chrome version on your desktop that's compatible with the chrome/webview version on your android device, usually this means having the same or higher version number on your desktop.

Kitkat marked the transition of android webview to be based on chrome but it wasn't made updateable.

Lollipop upwards have an updateable android webview which tracks the latest chrome version and isn't very far behind usually.