Even though I am for the eID I do share your worry but I don‘t think it‘s hopeless. Both politically and socially there are avenues to combat such over-identification. Still, most uses will probably more private than sharing copies of your ID so I am not sure what the gain for companies will be as it might just limit the customer base without much data gained. That does not seem in the interest of those companies. It‘s easier for the government to enforce certain checks, which is also not ideal but still there are avenues to fight this if it happens.