I was watching The Pacific and, while I do know a lot about other battles, I have yet to learn more about Peleilu. There was one part where they need to cross the airfield at Peleilu while the Japanese were firing into the American charge. During the charge, there is a cannon in a pillbox and the US Marines call in an airstrike. Why not just do that on the rest of the airfield structures?
I could see not wanting to damage the runways but why not just target the buildings? Why spend lives and possible failure on that?
After the battle, the assault on the island got a chilling nickname--Bloody Peleliu. The entire operation was far more costly than anticipated. Instead of taking the predicted three days to secure the island it took more than two months. The reason for this was a shift in Japanese tactics. Instead of opposing the landing at the beach and throwing everything they had into immediate counterattacks, the Japanese dug in and fortified nearly the entire island. As you can see in this map the assault began in the south, and seizing the airfield was an immediate objective. I haven't seen The Pacific, but it doesn't sound like the portrayal was all that inaccurate. There had been a preliminary bombardment, but due to the work done on the Japanese fortifications many of their positions survived. Until the assault began there was really no way of knowing just how costly it was going to be.
When the Japanese counterattacked with tanks there was an immediate response from naval gunfire and dive bombers. However, not every position can be attacked in such a way. In combat it can be very difficult to direct supporting fire onto a particular gun, especially when your support is coming from the air or from an offshore ship. As you guessed there was a reluctance to bomb the airfield itself, especially since most of the utility of the island was that airstrip. There is also the concern of the ticking clock. Perhaps you could pull back and call in supporting fire on the guns that are hitting you, but what is it going to cost? Sometimes taking the cost in casualties right now is thought to be less than the cost it will take to let that position keep firing until knocked out by air support or naval gunfire. This is especially true on Peleliu due to the entire assault being behind schedule from very early on.
Peleliu was a learning experience for the USMC and the American military overall. Future preparatory bombardments would be more extensive. Tactics that specialized in reducing enemy fortifications were developed. With their switch to defending in place from prepared positions the Japanese on Peleliu were able to inflict a large number of casualties on the Marines that landed there (roughly 1 in 3), but the American military eventually adapted to this shift in warfighting.
Robert Leckie (whom I believe is featured in The Pacific) wrote two books that I would recommend on the subject. Strong Men Armed is his history of the USMC in the Pacific in WWII. Helmet for My Pillow is his own memoir, and he recounts how he was wounded during the battle of Peleliu.