The audit log for modifications in a custom field does show the ID for it. The image below shows the audit log for a custom field:

This information is important, for example, when a problem happens to see what custom field caused it.

As an example, when a post function uses a custom field that was removed, it may cause an error. If the ID of the custom field was logged, it would be possible to know which entry of the audit log refers to the deletion of the custom field, by checking the ID.