Are Spirit types for traditions mandatory?

The answer to this question depends on whether you are using Street Grimoire or not. As you note, in the Core Rulebook, the spirit selection is merely a guide, but the individual practitioner is able to choose whichever spirit the feel is most appropriate.

However, in Street Grimoire it is stated more explicitly that the summoner cannot task a spirit with a task outside its domain. From Street Grimoire, Second Printing, Pg 41, first paragraph:

Mages of that particular tradition may only summon the spirits listed with that tradition, and they are restricted in the tasks they can assign them. Assigning tasks outside the general area of their tradition will not receive a response from the spirit (for example, a Buddhist mage telling an air spirit to heal him will get no response, as air is a Combat spirit in that tradition, while the Health spirit is earth).

No errata to date has clarified the issue one way or the other, but it is generally accepted (at least in my experience, and I think the devs had mentioned it as well, but don't quote me on that) that rules in supplements override rules in the core book when those supplements are used, on the assumption that they are replacing the appropriate sections with more detailed options, as well as being "newer". In other words, the supplements are expected to tweak some rules in the core book in order to allow the modifications and extensions they put forth.

So, if your table chooses to use SG, then that change (or clarification) is part of the package, though your GM can always choose to ignore it - most GMs I played with did, as it was overly restrictive and lead to some weird situations. For example, in the example in the book, the Earth spirit used by the Buddhist tradition for healing has no healing powers, optional powers, or skills. Of course, aside from Spirit of Man and their Innate Spell optional power, or Task Spirits and their Skill optional power, no spirit has much healing ability, making that a problem for many traditions even without the additional restriction, but almost all of them with it.

But as you've noticed, often one spirit is straight up better than another for certain tasks. Say you are fighting underwater, and your combat spirit is Fire. Even though you could summon a Water spirit, you are stuck with Fire because of your tradition. It's hard to imagine that this is intended, especially for a tradition like Chaos Magic, but RAW, it is the case.