Has the idea of point particles been thoroughly refuted?

Quantum mechanics alone is limited because, like nineteenth-century physics, it is still based on point particles, not super-strings.
In high school we learn that force fields such as gravity and the electric field obey the “inverse square law”—that is, the farther one distances oneself from a particle, the weaker the field becomes. The farther one travels from the sun, for example, the weaker its gravitational pull will be. This means, however, that as one approaches the particle, the force rises dramatically. In fact, at its surface the force field of a point particle must be the inverse of zero squared, which is 1/0. Expressions such as 1/0, however, are infinite and ill-defined. The price we pay for introducing point particles into our theory is that all our calculations of physical quantities, such as energy, are riddled with l/0s. This is enough to render a theory useless; calculations with a theory plagued with infinities cannot be made because the results cannot be trusted.
The problem of infinities would haunt physicists for the next half century. Only with the advent of the superstring theory has this problem been solved, because superstrings banish point particles and replace them with a string.

String theory may not be proven but has the idea of treating the building blocks of matter as point particle been thoroughly refuted?

String theory may not be proven but has the idea of treating the building blocks of matter as point particle been thoroughly refuted? For example Kaku writes:

String theory may not be proven but has the idea of treating the building blocks of matter as point particle been thoroughly refuted?

No. The infinities referred to in the quote were handled long before string theory was conceived, by means of the technique of "renormalization." The standard model is a theory of point particles, and is annoying successful in explaining the results of all particle physics experiments to date.

That said, you can view renormalization as saying that physics at the length scales we can probe experimentally is unaffected by whatever the actual physics is at much smaller length scales. That is, the "true structure" of an electron may be a point, or a string 10^-35 meters across, or a smiley face 10^-50 meters across, and we wouldn't be able to tell the difference: all these postulated structures are so small that they look like points to our experiments. Arguably, it would be more satisfying if the "true theory" consisted of objects of finite size, not points, so that calculations in the "true theory" could dispense with renormalization. But this seems like more an aesthetic principle than a refutation of theories of point particles.