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You are correct in that you only get the abilities listed; Paizo doesn't require investigation to unearth further traits. Also, few creature traits provide blanket immunities any more, i.e. "Construct" comes with none though in practice nearly all share a large set of immunities. This makes it easier to make exceptions.
As for the Elemental Form, it is only a form, not becoming an actual Fire Elemental. So you're going to fall short of some abilities which is something true for most every Form spell to keep their bonuses balanced while giving the player the desired imagery. You get as close as mechanically feasible for the spell level and again, only assume the form, not become any of the actual creatures.
Similar for the Familiar; You get as close as mechanically feasible for the feat/familiar-abilities spent on it. So yes, there could be a balanced version where you pay a higher level feat. PF2 stripped a lot of immunities from the game, so it'd be costly and I doubt people would pay for it, not on a Familiar.
The other two work it into their power balance too (which is why many complain about Summon spells being too weak, the caster's paying for those fringe abilities).
What factors went into Paizo's budgeting? I don't know.
There are some high level spells that achieve this, like Ferrous Form, but Fiery Body doesn't if you're focused on a fire form.
They really don't seem interested in publishing things that break core balance assumptions for how PCs work.