Adam Clarke on 1 Kings 15:14

The high places were not removed - He was not able to make a thorough reformation; this was reserved for his son Jehoshaphat.

Asa's heart was perfect - He worshipped the true God, and zealously promoted his service; see on 1Kgs 15:3 (note). And even the high places which he did not remove were probably those where the true God alone was worshipped; for that there were such high places the preceding history amply proves, and Jarchi intimates that these were places which individuals had erected for the worship of Jehovah.