"why do fundamental forces of nature exist?"
The force fields are emergent properties of simpler interactions between particles and photons (or bosons) acting over all possible paths and summed together.
For example, there are more ways that an electron and a positron can interact which end up with a closer position than which end up in a farther away position. The path integral gives an expected attraction.
So I think it is correct, if not fully descriptive, to say that all forces of nature are entropic. Gravity being less certain.
Its a bit like putting a red and a green gas together and saying that there is a 'mixing force' which causes them to mix together. It isn't really a force, just the most likely outcome from the huge number of possibilities (random movement of the molecules in this case).