Air carrier pilot reported being left high on descent into ABQ resulting in a 'low altitude' alert from ATC. Pilot expressed concern over lack of updates to ATIS and ATC keeping them high while on descent.

Narrative

While on the COLTR4 arrival into ABQ; the controller left us high; as we had been requesting lower and what approach to expect. We eventually requested relief; and it was approved to descend via; but were given relief on altitudes and speeds down to 10;000. We had RNAV 26 previously planned based on ATIS; so we then changed the setup to 08 based on current ATIS. We planned for 08 giving us the least amount of tailwind. Eventually ATC got back to us with runway 21 in use; so we changed the approach setup once again. When we checked in with ABQ Approach; we advised of our previous descend via clearance. ATC told us to expect the visual 21 and reduce speed to 250kts. We told ATC we were set up for the RNAV Z 21.We were told by ATC unable to give us RNAV Z 21 and turn heading 220 and maintain 12;000. We were then told expect Pilla and descend to 10;000. Passing the last mountain range we told ATC ready for Pilla. ATC said 4 miles from Pilla; cross at... low altitude alert maintain 11;200. We disconnected the autopilot to reverse descending to a climb; and both verified the terrain displays and visually out the window that we were SAFE. With only a few hundred feet to climb to 11;200 we reengaged autopilot; then were given a descent back to 10;000 as ATC cleared us direct Pilla; cross Pilla at 10;000 cleared for the RNAV Z 21.Cause: ATC left us high even while asking for lower. The approach in use was not updated in an ATIS. The controller was not speaking clearly; and was not decisive. The approach setup hat to be repeated multiple times in the terminal arrival environment.