Does a PhD student need a co-supervisor?
The direct answer is not a PhD students does not need a co-advisor. The problem here is to think about the role of co-advisors. I am sure the view on this varies so my view is coloured by situations with which I am familiar, which is the US and Sweden. Co-advisors may be involved because they have specific expertise that may be relevant to part of the work, for example specific investigations, lab work ec. Co-advisors may also be there to provide overall scientific expertise and provide feedback on written articles or the final thesis or both. Hence a co-advisor may not be very active when you start your PhD. At the same time by signing up as a co-advisor, I would expect the co-advisor to be open for discussion during your time as a student but it may fall on you to initiate such contacts when you need it. The main advisor is, after all, the one responsible for the direction of your work within your thesis topic.

So while one does not need a co-advisor, there are many instances where such support is necessary or at least very useful.