Usually functionalists and topologist have different points of view regarding physical and cultural milieus. Architects and urban designers have to start design process from a specific point. What do you prefer and why.
You may find if you read my publications, particularly How Designers Think, Design Expertise and most recently The Design Students Journey That these ideas are explored. In particular the concepts of primary generators and guiding principles will help you develop this argument.
I don't agree that architects and planners "have to" start design process from a certain point. They can choose among various departure points, problem/site analysis techniques or even define new ones. Would you rephrase your explanation?
If I understand your question correctly, I think the answer maybe 'argumentative'. In other words, it may not be a strictly 'yes or no' answer. It is subjective and contextual base question that needs to be satisfice differently for different cases. For instances, even the same architect or designer may have different starting point in the design process of a building (say, museum) depending on the specific physical and cultural milieus. These issues are one of the reasons why architecture seems more like a hybrid activity of science and art with good old common sense. Also, the architects and urban designers may not be a good comparison since the hierarchy and complexity levels of urban design and building or interiors design may differ significantly. Hence, their design process may differ although similar strategy and methods could be tweak to suit both purposes. Case in point, one may use the same design process (say, Double Diamond) process in designing a small interior or furniture or for designing a large university campus. The strategy of Divergence, Transformation, and Convergence may be tweak in both cases of design works. Various disciplines may involve different levels: components level (bed, chair, etc), product level (house, vehicle, etc), systems level (housing apartments, traffic, etc), community levels (city, town, etc).
Just try out and see if these process is applicable. Architectural building design strategies and methods by RIBA (1965) list the following steps of design activities, in sequence:
The same may be said about 'Rationalist' or 'Empiricists' architects design process and approaches. https://www.researchgate.net/post/Which_is_the_Way_Forward_Iconic_Rationalist_Architecture_or_Empiricist_Architecture_Icons
People have added to this discussion not just answers about primary generators, the original question, but also now guiding principles. Again you will find very thorough discussion of this in my books. The difference here is the a GP is held across projects although may adjust and alter over time. However a PG is only applicable to one project at a time.
interestingly designers learn more about their GPs by designing with them. This is the major way in which research through design progresses.
The starting point in a design process can have different initiatives; I can add another primary generator (As Bryan R Lawson mentioned) which is personal characteristics of the designer whether putting a sticker of functionalist or topologist on that.