well it's because we've always done it.
Categorically no! I use it because it is the right tool for my needs. Show me a better tool, and I would gladly switch, but there isn't one.
I'm sure the community on this forum are some of the most active users of GA, but even then how often do you _really_ utilise the data provided?
Every day. The information gleaned from analytics is invaluable.
Plus it must slow down the site
I doubt that the speed difference would have any significant impact on page speed. However, running a software of your own server that provides the same level of precision with the same speed as GA would certainly have a significant impact. But then I guess you could always setup a second server to handle your analytics.
Then there are raw logs and the software that runs stats on them if you want it.
Let me begin by saying that raw server logs are not just important, they are essential. Google Analytics does not replace those logs. Anyone that believes that because you have GA you don't need server logs is gravely mistaken. But analyzing server logs serves a different role.
GA is not perfect and one needs to be aware of its shortcomings. It is certainly possible to collect similar if not more data from your logs, but the amount processing and storage required would eclipse the size of server and database's used by most webmaster here at WW.
The most important thing to consider is that the data collect by Google with GA, is being collected regardless, through a variety of means such as the use of other Google services, as well as by Facebook by including their services, and by other third party services not mention by the users through the use Chrome. The difference with Analytics is that they give you access to the data collected such that you can use it for you own benefit.
So in conclusion, if you want to stick your head in the sand and pretend like Google isn't collecting data on your user's anyways then remove GA from your website. It really wont change anything either way. If someone can prove, with a repeatable, verifiable and falsifiable test, that eliminating GA does make positive difference, then please share.