I don't think these reasons are so strong. If you're not signed into Google, you don't need to worry about tracking. And you can turn off personalized results: https://www.google.com/preferences.
The Bang sytax is usually worse than doing a Google site search, since Google usually does a better job ranking a site's content than the website itself.
edit: I misread your comment about goog's site search indexing vs a site's native search. That is entirely site dependent. And it's still only a "kitten videos site:youtube.com !g" away in DDG.
I would bet money that Google "anonymously" tracks you regardless of whether you're logged in or not. And by anonymous, that's only until someone data mines the dozens of searches you do per day.