Entry into the bilingual stream is not based on the level of English but on overall grades (especially in German and Maths!). There are only limited places and entry into that class is very sought after, so only very strong students (regardless of their level of English) can join the bilingual option. So, if you have an international student with very good German and English (or French for the French bilingual stream) who is also very strong academically, yes, this is a great option.
I believe other public Gymnasien have it too, e.g. Wiedikon and Küsnacht. Usually starting in Kurzgymi, i.e. from 9th grade, not Langgymi (7th). With good enough grades and if the kid thinks it‘s cool: go for it.
I was under impression that after Gymiprüfung in canton ZH - there isn't choice other than kids get allocated based on distance / zip code to given school
Not true. Before you do the test, in Stadt Zurich you give your preference of the gymnasium in Zurich. The different gymnasium's have different 'profiles' - focusing on different study options/subjects.
Given you're in Wallisellen you're probably interested in Kanti Zürich Nord (KZN, see this page ) and Rämibühl. The latter also offers the International Baccalaureat, but there's no guarantee that they'll have space for you.
Speaking in general terms, KZN is a great school (even without the immersion option).
It's a big school, which means students have a lot of options for elective subjects - my daughter, for example, was there for the Fachmittelschule and one of her elective subjects was robotics and there was a mix of students from all streams in the school in the class.