Whether this is bad depends on your threat model. Additionally, you must also consider that other search engines are able to easily identify you without you explicitly identifying yourself. If you can't fool https://abrahamjuliot.github.io/creepjs/, you certainly can't fool Google for instance. And that's even ignoring the immense identifying potential of user behaviour.
Billing supports OpenNode AFAICT which I guess you could funnel your Moneros through but meh.