Archers get their own things, starting with a full extra attack that stacks with haste from rapid shot (greater rapid shot),
Well, for a feat they get Rapid Shot. And I don't know what greater RS is. Iproved RS removes the -2 to hit penalty, did you mean that?
being able to full attack things outside of charging range,
In practice that isn't often a major advantage IME.
the option to stay out of melee and do full attacks,
See above. Also, a good reach weapon + enlarged melee build with Improved Trip or Stand Still can also full attack and "stay out of melee."
the ability to split their multiple attacks across the battlefield, etc.
Would be awesome, if not for the whole problem of doing such low damage, they often don't have attacks left over once something does drop. I do have to say though, for my pouncing two-handed power attacking Bloodstorm Blade, who can mix melee attacks and thrown attacks together and treat the latter as melee for all purposes, the ability to always get his full attack even if he runs out of nearby foes is nice. But...only because he actually has the killing power to benefit from it.
At high levels spending hundreds of gp for a strength bow or anything else is trivial.
The cost is only one problem. A much bigger issue is how big a pain in the ass it is that it can't auto-adjust or at least have a larger "grace period" of below the str rating before it's unusable. Any time you're hit for str damage, anytime you have the gall to expect the full benefit of an enlarge person spell (I mean, you only suffered -2 to hit and -1 AC, not like you sacrificed much for the str bonus and worthless reach)... just...grr! These are very far from uncommon events.
A bow is easier to sunder than a sword (5 hardness versus 10 and 5 hp versus 10 before the bonuses for enhancement). A sword is easier to rust than a bow.
And a bow can be warped by warp wood and set on fire. Meh.
At high level getting a bunch of +1 bane arrows is a viable fairly cheap strategy. Or arrows with an elemental enchantment different from the bow for stacking goodness with lower cost.
It's ok. I'm a cheap bastard and am hesitant to event blow a low level potion, so I wouldn't use that option much, it's still over 100 gp per arrow. But at high levels it's decent to get some bane arrows.
More times than not our archer was our most effective combatant.
Good for him. How much damage is he doing a shot? How does he deal with DR? Wind Wall? How is your Eldritch Knight not doing more damage than him?