As you know, if a thing is useful or not depends upon context. If you are hungry, will a 4096-bit RSA key with a CAMELLIA256 subkey be useful? Not really, except perhaps as food for thought.
One-time pads are being used at this very moment by serious and perhaps dangerous people all over the world. OTPs work. Ciphertext encrypted with a one-time pad can be heard on HF radio all the time. Is it useful? Certainly. The question is: "for whom?"
Why are one-time-pads useful? You don't have carry around a lot of equipment. Paper does not leave an electronic trail. Paper burns. Little pads are easy to hide. It's hard to get a kleptotrojan into a pencil. Paper is cheap. Vernam cipher is the perfect cipher if the key is truly random, the key was protected, and the key is as long as the message. When your equipment stops working you can pull out the little book and figure out a way to deliver your message--and its content will remain private. You can actually see the key destroyed. When you destroy it, it's really gone. Everything about using a one-time-pad is easy to understand. A one-time pad does not require electricity. If you lose your pad, that might be bad, but you don't have to revoke it in front of everyone. All of that sounds very useful, right?
So, to answer your question directly, "if we can find a suitable, secure way to generate and share unique keys, does the Vernam cipher become useful?"--yes, it already is very useful to certain people all over the globe, but they are not talking about it.
"Is there anything else that needs consideration in this respect?"
It isn't that the key "should not" be used again, as if it were an option. It must only be used once.
The key must be at least as long as the plaintext.
The key must be truly random in order to be perfect.
The key must have been protected against damage or compromise.
The key must have been shared via a secure means.