AFAIK there is no mandatory @2000ft at the IAF. There is however a minimum safe altitude published for the initial segment.
Some STARs where I work have minimum safe altitudes of e.g. 5000 ft on two consecutive segment split by a waypoint with a hard constraint of @FL90.
The minimum altitudes are just to show at what altitude the procedure is protected in relation to terrain, and in some cases airspace.