Once your email is out there, there's no going back.
Email addresses are personally identifiable information, and revealing a relationship between a business and a person is potentially very dangerous.
For example: http://www.bbc.co.uk/news/technology-36247186
If you look at the past 5 years, there is almost not a single major website that hasn't been hacked and hasn't leaked personal data. Not only do I see no sign of improvement, but it is rather accelerating. Leaking information on 30m+ people is now becoming common and barely makes the news outside of a few specialized websites like HN.
If you have a better alternative than feeding garbage data to websites who want to collect data they won't need (why would an online retailer give a shit that they are shipping a product to someone called Mr X rather than Mr Y?), I want to hear it.
(There would probably not be a fine; the company would be investigated and warned by the various regulators).