Matthew Poole and continuators on 1 Kings 15:14

14 But the high places were not removed : nevertheless, Asa his heart was perfect with the LORD all his days.

Obj. He did take these away, 2 Chron. 14. 3. Ans. He took away those which were devoted to the worship of Idols, as is there said, he took away the altars of the strange gods, and the high places, to wit, where they were worshipped: but as for those high places where the True God was Worshipped, he did not take them away; partly, because he thought there was no great Evil in them, because they had been used by David and Solomon, and other Good and Wise men; and because the True God was there worshipped, and that in the manner, though not in the place, which God had appointed; and partly, because he thought the removal of them might do much more hurt than their continuance, to wit, by occasioning the total neglect of Gods Worship by many of the People, who either could not, or through want of competent Faith and Zeal would not go up to Ierusalem to Worship, now especially, when the Israelites, their near Neighbours, formerly their Friends, were become their Enemies, and watched all opportunities to invade or molest them, which they concluded they would do when all their Males were gone up to Ierusalem; and partly, because the People were so obstinately bent towards them, that it was, or at least, seemed to him, impossible to remove them without great offence, or such commotions as were highly dangerous to that Church and State.

i. e. He did sincerely and constantly adhere to the Worship and Service of God. Though he could not hinder the People from using the high places, yet he did intirely Devote himself to the Worship of God in the manner and place prescribed by God.