As soon as you have to deal with users with a radically different alphabet/input-method, the wheels tend to come off. Can your CSR reps pronounce names written in Chinese logographs? In Arabic script? In the Hebrew alphabet?
And even if you could, I don't know if you actually do it by looking at what you signup form asks me to input.
In any case, the proper way to handle this is to store the name as originally written, and have the app that CSRs use provide a phonetic transcription. Coincidentally, this kind of stuff is something that LLMs are very good at already (but I bet you could make it much more efficient by training a dedicated model for the task).
Add to that that natives of non-latin languages are already used to this.
For better or worse, English and therefore the basic latin script is the lingua franca of the computing age. Having something universal for internation communication is very useful.