I'm personally not particularly obsessed with getting rid of every last trace, but I do think we should be mindful of how many places large companies like this have influence of some kind, and how much we depend on them for this or that.  With regards to Google in particular, there was a time when I felt like they basically owned and defined the internet because they were the sole provider of so many kinds of new and vital services.  Whether or not that was a valid feeling or not, I can't say, but at least as it stands currently, I strongly feel that is not true.  I've personally cut my use of their services dramatically to the point where watching youtube is the only thing left.  My goal wasn't to eliminate my use of them, just reduce my dependence as much as possible, in terms of "account services", like email, etc. and I feel I succeeded entirely at that.  Things I can do without an account don't bother me particularly.

Google does practically own everything. Any decision that they make, concede, or barter for affects every smaller provider. Example: YT's copyright system.