I honestly think they would. None of the other options are feasibleLeave Google as the default anyway just to throw a middle finger at the government.
Bing - terrible.
DDG - I find terrible, others seem to like it, but couldn’t handle the traffic increase.
Kagi - paid; non starter. Couldn’t handle traffic
Anyone else?
Plus search engines are going the way of the dodo. This remedy is addressing a problem that the market is already solving.