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They actually do. It's just that the mass deficit creates the nuclear binding energy (or nuclear glue) through residual strong interaction (strong force) that overcomes the coulomb force that's trying to push the nucleus apart and keeps it together. The electrostatic repulsion between protons doesn't just disappear when nucleons are fused together to make heavier atomic nuclei.
We can see the electrostatic force pushing atomic nuclei apart as we look at the top of the periodic table. When we synthesize heavier and heavier elements in the physics lab, they are more and more reluctant to "stay together" and stabilize. And we finally reach a point where we just can't force a super heavy nucleus to even begin to stick together. Not even for the tiniest fraction of a second.
Because they are positively charged and like charges repel each other.

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Proton repel each other.
But neutrons that are neutrally charged occupies the space between two protons and avoids repelling of protons.