Giving write access does not mean giving unrestricted write access
Also, another way (which I built in a previous compagny) is to create a simple certificate provider (API or whatever), integrated with whatever internal authentication scheme you are using, and are able to sign csr for you. A LE proxy, as you might call it
It also sounds like the right people to handle certificate issuance?
If you are not in a good position in the internal organization to control DNS, you probably shouldn't handle certificate issuance either. It makes sense to have a specific part of the organization responsible.