Some quick rules to make Elementals less bizarre:
All Elementals gain No Breath and Immunity (Disease).
Air Elementals have the Aerial template graft, regardless of CR, and lose the extraplanar subtype (except when granted it by Aerial). This does not reduce the elemental's fly speed. Air Elementals treat Acrobatics as a Master Skill. Swap their Dexterity and Constitution bonuses and Fort and Ref saves. Note that this also changes their initiative.
Earth Elementals have the Cthonic template graft, regardless of CR, and lose the extraplanar subtype (except when granted it by Cthonic). Note that this means Greater and Elder Earth Elementals upgrade their Blindsense (vibration) to Blindsight (vibration), without reducing the range. Earth Elementals treat Athletics as a Master Skill.
Fire Elementals have the Fiery template graft, regardless of CR, and lose the extraplanar subtype (except when granted it by Fiery). This does not change Burning Strikes. Fire Elementals treat Acrobatics as a Master Skill. Swap their Dexterity and Constitution bonuses and Fort and Ref saves. Note that this also changes their initiative.
Water elementals have the Aqueous template graft, regardless of CR, and lose the extraplanar subtype (except when granted it by Aqueous). This does not reduce the elemental's swim speed. Water Elementals treat Athletics as a Master Skill.
The biggest effects here are that the various elementals are drastically more able to function in their home environments. I may revisit this to bring them even more in line with the Combatant array, which they have some strange interactions with (such as the CR 1/3 and CR 1 elementals having +1 EAC for no apparent reason), and/or the rules covering their home environments, to ensure they can function in them.
The "Elemental" stat blocks are actually used as the basis for all summoned monsters in Starfinder per Alien Archive, and are just templated into whatever. Which is why they're so lackluster, and why they're not extraplanar by default. Though honestly I think it makes perfect sense for elementals to be born of the Prime, especially if you're not using the "traditional" D&D cosmology; in most non-D&D fantasy media, elementals are more like either fey or constructs, rather than aliens from another dimension.
Why would elementals not be considered extraplanar? They *are* extraplanar.
No, they aren't. A Fire Elemental on the plane of fire is a native, not extraplanar. Extraplanar, in general, should always be a subtype acquired only when a creature eligible for it is outside of their native plane.