I understand where you are coming and I agree it gives Google (or Bing) more power, but ... it was the user's choice to give Google (or Bing) that information by using it as a search engine.
If they gave the information to you too, it likely goes to you, but also to the other 50 .js files you include from various sources of dubious trustworthiness which every site these days includes.
Furthermore, what you are saying is "this admittedly private information used to be available to all and it was useful for some, now it's only available to the entity the user specifically gave it to, and that's bad because the few who actually used it for good don't have it". But the whole idea of GDPR (and similar) laws is to put the control back with the user, which is a good thing.
I think some standard with which the user explicitly lets the website know "yes, the search engine query that brought me here is X and I allow you to have it" would be good, but I don't think dropping this info from the referer (sic) is bad.
If they gave the information to you too, it likely goes to you, but also to the other 50 .js files you include from various sources of dubious trustworthiness which every site these days includes.
Furthermore, what you are saying is "this admittedly private information used to be available to all and it was useful for some, now it's only available to the entity the user specifically gave it to, and that's bad because the few who actually used it for good don't have it". But the whole idea of GDPR (and similar) laws is to put the control back with the user, which is a good thing.
I think some standard with which the user explicitly lets the website know "yes, the search engine query that brought me here is X and I allow you to have it" would be good, but I don't think dropping this info from the referer (sic) is bad.