A C172 pilot reported they ran off the end of the runway after landing and the prop struck a runway light. The reporter refueled and departed to their destination in spite of the prop strike.

Narrative

The incident aircraft suffered a prop strike after landing. The incident aircraft overran the runway after touching down and the propeller struck a runway light. There were no injuries to the pilot and two passengers. The incident flight was a refueling stop at ZZZ on the return back from ZZZ1 to the plane's home base at ZZZ2. The flight path was along the shore. Post departure; the pilot requested VFR flight following and was in ATC communication with ZZZ approach; ZZZ1 approach; ZZZ3 tower; and back to ZZZ1 approach before terminating flight following and switching to ZZZ CTAF.The approach was a straight-in approach to runway XX continuing from the direction of the flight. The approach was well stabilized; descending from 1300 ft AGL 5nm from the threshold to 400ft AGL 1nm to the threshold at about 300-500 / fpm. The plane crossed the runway threshold at 30ft AGL and 83kts IAS. There was one other aircraft in the pattern. The plane touched down on the main gear about 1000 ft from the runway 28 numbers; and the pilot applied aerodynamic braking and brakes. Due to the energy into the landing; the plane had not slowed down to a safe taxiing speed in the judgement of the pilot. The pilot decided to continue straight ahead into the grass rather than attempting to turn at a potentially high speed. In doing so; the propeller hit a runway light at the end of the runway. The engine and propeller continued to function without any noticeable degradation and the pilot turned the plane around onto the runway and taxied to the fuel pump.Other legs in the flight. ZZZ2 - ZZZ1. The first leg of the flight was ZZZ2 - ZZZ1. After takeoff; the pilot experienced radio communication issues in talking to ZZZ4 tower. The pilot had done a radio check on the ground prior to taxiing and coordinated with another plane on the ground about the order of the departure. The radio issues caused the pilot to reroute the flight as the planned route was to go north via a route; and then turn east along the shore. However; ZZZ4 tower reported the transmissions as unreadable and denied entry into the Bravo. The pilot spent a few minutes trying alternative solutions; including using the passenger side PTT; and approaching closer to a bridge for potentially better reception. After multiple failed attempts in establishing communications with ZZZ4 tower; the pilot proceeded to fly an alternate route which had been briefed for the return leg - flying under the Bravo and then along the shore. The pilot requested flight following from ZZZ1 approach; which picked up the radio transmissions without any issues and further communications were unremarkable. The rest of the flight was uneventful; landing at ZZZ1 runway XX. On the ground; transient parking was in the grass rather than asphalt. After the refueling and despite the prop strike; the pilot elected to continue to the original destination of ZZZ2. The flight performance was not noticeably degraded. The plane was tied down and the pilot and passengers departed the airport. Total flight experience: 155 hours PIC hours: 67 hours. Last 12mo: 16 hours Last 3mo: 5 hours.Contributing factors to the incident. The incident came after 2.7hours of flying; which is the higher end of the range of flight lengths for the pilot; increasing the likelihood of fatigue settling in. Running behind the originally planned schedule; including due to the radio issues at the outset; induced get-there-itis in the pilot to complete the planned mission. Physical fatigue settling in due to the hot and humid weather.Decision to continue the flight after the prop strike: The prop strike was a major shock to me; the pilot. A combination of shock and shame of having damaged a valuable shared resource; having put myself and my passengers in danger; and get-there-itis led to a major lapse in my judgement in deciding the continue the flight back to its home base. Post the prop strike; the engine had not shown any obvious signs of damage; had taxied fine and started up smoothly. In this stressed state of mind; I was in denial about the un-airworthiness of the plane and made the decision of flying back to the home base and figuring out the consequences back at the home base.