SR5, page 302 outlines what you can have an unbound spirit do for you for a single service, one of which is to fight at your side in combat. Any spirit can fight for you if so ordered. As for bound spirits, they can be told to do whatever any unbound spirit can be told. In fact, only one type of service of bound spirits even mentions a restriction to a category: Aid Alchemy, Sorcery, and Study. That's it, that's all where spirits are truly limited in what they can do (a shaman can't learn a detection spell from a beast spirit, or anything from a fire spirit). Heck, a hermetic can order a bound water spirit to sustain a Detection spell. Maybe it won't like it, but it'll do it.
The quoted section in Street Grimore, I say, is poorly written at best. Besides an Aid Sorcery action, how does an earth spirit help a Buddhist in healing? Default on a First Aid skill test (as Medicine & Biotechnology can't be defaulted on)? "Paging Dr. Zoidberg!" The Guard power that both air and earth spirits (and many more) have access to can help in health related instances, but apparently for the Buddhist it's only useful in a health related way (it isn't useful directly for healing); guess it's only useful for an air spirit in a fight somehow, which seems limited to preventing the use of Accident in a fight or negating glitches on your combat or defense tests. On that same logic it's a really good thing that fire spirits have Search as an optional power, or they'd really suck at finding things for Aztech magicians, short of burning down everything around them (needle in a haystack? no problem, burn down the haystack). Especially considering that beast spirits have a battery of enhanced senses that'd help make them excellent trackers over fire spirits, especially if it came to finding something in a deep lake (it'll help you retrieve it, but it won't help you find it in the first place). Oh, hermetics might as well not bother calling up a spirit of man with an Invisibility spell to use, since it's a Health spirit it won't ever use it since Illusion magic is "outside the general area of their tradition." Might as well stick to Heal or Increased Reflexes instead since those spells are within its area of the tradition.
And if you really took that section in SG, page 41, literally it'd also make the Spirit Expansion metamagic (Forbidden Arcana, page 41; lets you summon a spirit from outside your tradition, legal & RAW) worthless as each additional spirit doesn't conform to any of the five categories, letting them tell you to frag off for being asked of anything you want one to do (a hermetic summons a new guidance spirit to track down a missing person; nope, not the summoner's Detection class spirit, not gonna do it). As Rosa pointed out on the previous page, going very literally here would make spirit aid for Elder Gods magicians suck (Task are ill suited for combat). Drakes of the Draconic tradition, on the other hand, would be OP as any spirit type will do anything asked (they can conjure all spirits that don't have Inhabitation or Possession for any category of magic); that summoned beast spirit will help track down a known criminal (Detection), help batter down that barricaded door he's hiding behind (Manipulation), as and then fend off any bodyguards he's hired for protection & muscle (Combat).