If you want analytics, anonymize first and then use whatever tracking you want. But first price that your anonymizing is really effective, even if they results in less precise tracking.
It is a huge difference. There's one thing to have your data stored on a server that only one person has access to, and they are obliged to respect strict privacy laws and a completely different thing to have your data sent and shared to hundreds of companies that can use that information for various marketing or analysis purposes.
I really disagree. Whether the cookie shows under a dns name or another means next to nothing as to who is doing the tracking. If I'm not mistaken, Google Analytics is now pushing to have all cookies served by a front domain, hiding from the user who the third parties are. I may be wrong on this, have not done my research yet.
There's one thing to send your data to Google and accept for it to be processed by them and all their partners and another thing to send your data only to the company that owns the website that you are currently visiting and only allowing them to internally use this data, without it being sent or processed by any 3rd parties (as strictly specified and regulated by the privacy laws).
I think it's a huge difference between:
A. I track visitor stats and usage details and send all the details to Google and their partners (which enables them to create a profile of the visitor across the web, have in-depth stats about your website's traffic, traffic sources, sales, visitors demographic, use the data to target specific or groups of visitors or share it with your competitors or other companies for marketing purposes).
and
B. I track visitor stats and usage details, store them locally and use them to improve my website.
Now you can take a guess how many actually do either of those two things... I would not even put it at above 1%.