2 Kings 14:4 (ESV)

4 But the high places were not removed; the people still sacrificed and made offerings on the high places.

The result was that the high places (places for sacrifices) remained in existence. His servants even offered sacrifices and burned incense there. Place this next to 2 Kings 11:18 – 12:4. The image that emerges is one of love for the temple of the Lord and turning a blind eye to the service to the Lord in other places. Looking at the destruction of the temple of Baal (2 Kings 11:18), it is not likely that idols were worshipped on the high places (of sacrifice). But since the temple of the Lord had been built, the people were commanded that the Lord be worshipped there (see Deuteronomy 12:4–6).

The Canaanites worshipped their gods in various places of sacrifice, and for the servants of King Amaziah there was the great risk that, despite their intention to worship the Lord on these (high) places, influences, and tendencies of their (former) native religions could creep into their worship of the Lord. So, the problem of offering sacrifices on the high places is in the first place that it is not in accordance with God’s command in Deuteronomy 12:1–32; and in the second place that it creates the risk of mixing their worship to God up with heathen religious practices.