The mass deficit is due to the potential energy loss.
But, why there are potential?
Coz there is a force associate with a potential.
Or in more correct way, the potential energy is due to the force. When 2 bodies in space has a attractive force, then it naturally go together. And the force accelerate the body and increase their kinetic energy.
Thus, we think the force created a field, which stored potential energy. When the force accelerates body, the potential energy converted into kinetic energy.
Imagine there are 2 bodies, A & B, Which at different location and have different force. If A is further away, when it comes at B, it has more kinetic energy than B, coz B is at rest at that position. Thus, further away, higher the potential.
Can thus potential be as high as infinite? In reality, because thing has surface, has size. The minimum distance between the 2 bodies is the sum of their radius. And if we sum up all potential, from the surface to infinity. We found that it is finite. And we like to set the potential at infinity is zero. Thus, it makes all attractive force has negative potential.
But, electric and positron do not has size, so, and electron and a positron can come together and the potential energy they can release is infinite! Since when they are apart infinite and the attractive force accelerate it, when they meet, their speed will be infinite!
Wait! The speed cannot be infinite, the highest speed is the speed of light and for an object has mass, it never move at the speed of light!
So, when electron and positron hit each other from infinity. However, relativity does not limit the energy and the kinetic energy. The result is, it can release infinite energy.
But at first, infinite exist. In reality, we can just approximate the “infinite” by far far away. When the potential change very little. But far far away is still very short compare to infinite. Thus, we don’t have infinite energy source.
In laboratory, we can accelerate electron and position at very high speed and contain several GeV. Thus when those particles annihilate, they release GeV energy due to the kinetic energy and their mass, which is just 0.000511GeV. Does not help much.