It is expected that pair potentials go to zero for infinite distance as particles that are too far apart do not interact.
Other potentials, like the Coulomb or gravitational potential, are long range: they go slowly to zero and the contribution of particles at long distances still contributes to the total energy.
The total energy expression for pair potentials is quite simple to use for analytical and computational work.
It has some limitations however, as the computational cost is proportional to the square of number of particles.
This might be prohibitively expensive when the interaction between large groups of objects needs to be calculated.
In some cases it is necessary to calculate the interaction between an infinite number of particles arranged in a periodic pattern.
Pair potentials are very common in physics and computational chemistry and biology; exceptions are very rare.