Grundfos GRU-595916 595916 https://www.amazon.com/dp/B000JG81AQ/ref=cm_sw_r_cp_api_i_WJASNME9NR7MQEGRPQ23
Buy and install something like this! Allows you to pre heat your water without wasting it. This one has a mechanical timer but there should be digital ones as well. Works well if you shower at a similar time each day
Your right it would not make the water get there any faster. Your wrong about the temp being dangerous unless you have young children or your an idiot who drinks out of the hot side tap. The owner should just spend $$$ on a Grundfos comfort pump with a crossover valve.
Grundfos 595916 1/25 Horsepower Comfort Series Recirculator Pump https://www.amazon.com/dp/B000JG81AQ/ref=cm_sw_r_cp_api_EvERAbPYBHYM8
I did say try the thermostat first btw.