Cochlear implant are designed with electrical signals directly to nerves but needs therapy to understand. Its akin to a legless person learning to walk again with new metal legs. Has similar issues as above with noise, etc, but the nerves are stimulated directly which allows more accurate hearing but not 100%. A major downside is that you lose 100% natural hearing in that ear as the nerve stimulation wires go inside the cochlear, effectively blocking any sound from going in. So imagine you lose a foot, and they offer you a metal leg to walk again and that requires therapy. Its a tough choice for some: some natural hearing or accurate but stimulated hearing.
Then the ear implant. Or really a natural cochlear implant is akin to attaching a new human leg to a legless person. Still, there's therapy needed. However, the cochlear is around the skull. So it's not as simple as taking it out and reattaching it. A lot of research is being done with promising results.
Later, the bionic cochlear, a complete electrical replacement of cochlear where you hear as well as a dog, but that's a dream.
The ideal solution would be to repair the hair cells or replace them with a drop-in solution that restores their function. Likewise with the auditory nerve. Of course, these are pie-in-the-sky ideas currently.
Sound amplification essentially symptomatically resolves the problem by playing the appropriate frequencies louder, but in the case of hearing loss due to damage, amplification would just exacerbate the problem, unless I am fundamentally misunderstanding something.
In layman's terms, it would be like temporarily losing your hearing by going to a rock concert, and then raising the volume of everything around you to rock concert level, so you can continue to hear things.