37 degC is not universal and we certainly don't "choose" this temperature. Evolution does not "choose" (as if consciously) to make things happen in a certain way. There is a wide range of body temperatures among animal species, from poikilothermic to homeothermic. Even among the homeothermic species not all of them have a body temperature of 37 degC. For example, birds and small mammals tend to have a higher body temperature to support a higher metabolism as required by their life styles. If you check a baby's body temperature it is higher than 37.
You have answered your question- it's the Hydrogen bonding that has made us evolutionary choose to thermostat our body at 37 degrees.Beyond that temperature,most of our enzymes systems don't work & they become physiologically ineffective.
The question might be better phrased more broadly: Why do endothermic homeotherms, including mammals, birds, and flying insects, as well as desert reptiles that show behavioral thermoregulation, generally maintain a core body temperature between 30 and 40 C? This has been debated in the physiology literature for decades and there is no clear answer. One hypothesis is that this is the middle of the Kelvin temperature range between the freezing and boiling points for water (~ 303 - 373 K) and is optimal for various physical properties, such as density, viscosity, pH, etc. Another hypothesis is that a body temp in the mid-30s is greater than air temp in most terrestrial environments, which means heat can be lost through conduction, convection, and radiation, without requiring evaporation of water. The bottom line is, we don't know.