Corneas are donated and transplanted, but not the eyeball.
I don't understand. What is the purpose of donating a cornea without an eyeball to a blind person?
No-one can re-implant an entire eye, because the optic nerve has been severed in one who has lost an eye. A cornea can't be grafted to a glass eye. But blindness isn't only caused by loss of the entire orbit. It's also caused by cloudy corneas, which is the purpose of eye-banks.
The optic nerve is a cable of nerve fibers that carry visual information from the eye to the brain. In adult mammals, any damage to the optic nerve caused by injury or disease tends to be permanent, because the cells that form the optic nerve cannot regenerate. Any injury or disease that involves optic nerve damage can lead to permanent loss of vision. Obviously the loss of an eye would sever the optic nerve.
However, if the future holds success for optic nerve regeneration, it would also open the door for entire-eye transplantation. In which case, a new cornea might come in handy.
You are asking two questions that you think are connected but are actually not.
Question 1 - What is the use of eye banks?
Answer: It's to store corneas for transplant for people with cornea damage.
Question 2 - What use is cornea transplant to a completely blind person?
Answer: It depends. If the blindness is due to clouded cornea (several diseases cause this) then replacing the cornea will reverse the blindness. If the blindness has other causes then cornea transplant is of no use to the person.
I used to work at an eye bank so I have a bit of knowledge about this, though some of it may be out of date.
There are several aspects to an eye bank. The corneas are one of the primary things that are kept for transplantation. Of course, this will not repair blindness in someone that has problems in other areas of the eye, but corneal transplants are helpful for people who have corneal damage for one reason or another (such as a foreign object, age, or disease damaging the cornea.)
Beyond this, small parts of the sclera (the white part of the eye) are also sometimes used to patch damage (though generally this is not because of unexpected trauma, but because of reconstruction from other surgeries, such as valve implantation because of glaucoma.)
Finally, of course, many people would not understand what the purpose of the organization was if it was called a "Cornea Bank". "Eye Bank" is more descriptive.
The eyeball is basically the sclera that surrounds the delicate inner structures of the eye (see wiki on the eye). The cornea is the transparent window in front of the pupil that transmits light to the retina. It needs replacement when it turns opaque, often due to damage or infections. The cornea can be replaced on its own, without the need for transplanting other tissues of the eye, as an opaque or otherwise damaged cornea does not necessarily mean that other structures of the eye are damaged. If the light-sensitive parts are damaged, including the exceptionally rare case that the entire eye ball is missing, corneal transplants have obviously no use.
Eye banks are necessary to properly retrieve and store eyes. They extract, preserve, and dispatch corneas when necessary (eye bank wiki).
In addition to providing tissue for transplant, eye banks also provide tissue from all parts of the eye to medical schools and universities for teaching and research purposes. There are many medically relevant questions that can only be answered by examining human tissue, and eye banks facilitate this research.
It seems to me that really your whole question seems to be much simpler than it seems and it is just
"why are eye banks called eye banks when they can't transplant eyes, just bits of them like corneas"
The answer is:
In the english language and in various cultures, the names of things often have a loose and not entirely accurate relationship to the product at question. For example a person might be a screw loose mentally but that doesn't mean a physical screw, etc, etc.
English is not a consistent scientific logical language for describing the world.