Air Traffic Controller reported that a Local Controller having a departure off a parallel runway whose flight path would cross the parallel runway resulted in a departure being assigned an altitude below the MVA to separate the aircraft.

Narrative

Aircraft X was on an IFR practice approach to RWY 17L with missed approach instruction to fly rwy heading climbing to 2000. Local was briefed about this while the aircraft was on 8 mile final. Aircraft Y was rundown awaiting IFR release for RWY 17R. I was dealing with a getting a flow time for on ground control when the takeoff clearance was issued for Aircraft Y on the FTHIL3 departure turning Aircraft Y across 17L centerline. I did not hear issuance of the take off clearance to know if an instruction was given to separate Aircraft Y from Aircraft X missed course. When I looked back and saw Aircraft Y rolling mid field 17R with Aircraft X crossing the threshold for 17L; I verified that local knew Aircraft X was IFR straight out to 2000. Local said yes. Local then told Aircraft Y to start their left turn leaving 2000 and Aircraft X to maintain 1000. 1000 is below the MVA of 1700. The aircraft were less than 2 miles and 1000 feet; with one of them stopped below the MVA. Traffic was never issued.Aircraft should not be issued departures that require them to cross the centerline of the parallel RWY when using that RWY for arrivals. Additionally; timely briefing and implementation of the new SOP (it was supposed to be implemented over a month ago) would have prevented this. The new SOP has preferred departure RWYs based on direction of flight.