Pilot reported a near miss during short final approach with a departing aircraft on the runway that the Tower Controller had cleared for takeoff. Pilot executed a go-around.

Narrative

Performed one takeoff and full stop landing/taxi back on runway XXR in Piper Arrow with instructor aboard. Subsequent takeoff on XXR in right traffic pattern as directed by ZZZ Tower. ZZZ Tower told us after we were established on XXR crosswind leg (right traffic pattern) to expect landing on XXL. During downwind to base turn; ZZZ tower cleared us to land on XXL and issued 'caution wake turbulence' from departing biz jet on XXL. Biz jet holding short at XXL cleared to take off by ZZZ tower as we were on short final for XXL at 1/4 mile and 200 feet AGL. Had we continued on to landing as cleared by ZZZ tower; we would have landed on top of biz jet that was just beginning its takeoff roll. We executed a go-around to avoid landing on top of biz jet. We reported go-around to ZZZ tower and was told to execute mid field left turn to engage in left traffic for XXL. We continued to normal left traffic pattern and landed on XXL. No acknowledgement by ZZZ tower of near miss. I called ZZZ tower after landing and spoke to unknown; unidentified person who answered phone. I advised we were in a near miss situation and asked for an explanation. This person stated they had to get the biz jet out as 'their clearance was about to time out'. This airport has seen a tremendous increase in student pilot traffic in the last two years and tower has a problem managing traffic flow. Their excuse (as reported in aforementioned telephone call) is 'we have been burned too many times but student pilots'; and their admitted solution is to treat all SEL pilots as student pilots. They obviously have a problem with flight school instructors not properly training student pilots; which ZZZ tower administrators fail to address. This has been an ongoing issue for the past year.