The proton-electron model for the atom has a fairly straight forward explanation for radioactivity in materials.
Large atomic nuclei are not big round balls with protons and electrons tossed together. They are more like crystals, with arms branching out and bending off to the sides.
The core of these structures carry an overall neutral charge while the tips carry the positive charge. This means that the tips of these structures repel each other.
As we go higher in atomic number, these structures start bending in on themselves. The branches get too close to each other, and the tendency is for these to break apart.
Atomic nuclei falling apart in this manner is what we refer to as radioactivity.
This problem does not arise suddenly at a certain atomic number. There are two radioactive materials with atomic numbers less than lead. These are element in which no stable configuration can be found despite their relatively small size. There is an arm that comes out in the wrong direction. For that arm to point away from its fellow arms, it needs to have one more or one less proton.
Beyond lead, there are no stable elements. They are all radioactive to some degree. The arms are turning in on themselves. There are no way to arrange them into stable structures.
Part of the problem is the relative size of protons and electrons. There is a whole lot of proton for each electron. There is a lot of mass to keep in place, and if mass condensation is real, as it appears to be, then this problem is likely to increase over time.
As protons grow in size, they become harder to keep in place inside the atomic nucleus.
Materials that are inert today may become radioactive in the future. Materials that are radioactive today may have been inert in the past.
The overall tendency is for matter to become more radioactive over time as mass condenses onto the proton.