Were you looking for ID or for birth certificate? I know its possible at least in WA state to get a replacement birth certificate online.
ID. I did note there are a couple states that allow you to order a birth certificate replacement online; Washington State uses Vitacheck to order certain certificates and things like birth, death, marriage etc are public records. Again, I only checked 10 states to verify you had to be in person to get a state issued ID (probably because they want to take your picture and do not accept you sending one in). Ohio, where I live requires These forms of proof that you are who you say you are to vote. I will not note the unexpired Ohio driver's license is questionable; who cares if it is expired? As long as you match your photo and have a current bill with current address (if it differs from the driver's license) then you should be fine. Just because you no longer drive does not mean suddenly you have become a different person.
One of my biggest complaints with our country (and one of its strengths) is the separation of states from federal entities. IMHO, if we were simply issued a centralized USA identification and then endorsed it electronically with drivers license, voter registration, social security and standard other items, we can then issue free photo ID's to everyone. DMV's, social security offices could be issued the ability to print new ID's for people. Obviously a federal agency as the ID was prepped and programmed could reach out to a state API to pull its endorsements for the individual and the feds could offer the same for DMV's or state offices issuing federal side of the ID.
How would this help with the voter ID requirement? Grass root organizations can help "poor" people obtain their valid government issued ID. First time registration is going to require some additional proof, usually utility bills, birth certificate, paystub, header of a bank statement etc. But we _NEED_ to sort this crap out. I have no problems with voter ID's as long as we provide a way for people who a) do not drive, b) do not have a current ID obtain one at no expense to themselves.