Looks like a workaround. However, there is at least one known caveat to this.
When in PMs, people tend to say things that they wouldn’t say publicly. Once such PM messages exist, we cannot make the private topic to a public category.
There are other drawbacks as well:
The category looks less dynamic
A lot of additional manual work: a) people who come for the first time don’t even know that a private topic can become public; b) veterinarians will have to not forget to click on “Make public”, or ask mods to do so
If I put detailed instructions, no one will read them, at least not when they interact with veterinarians for the very first time.
Most ‘popular’ forum platforms I have used can do this - at least vBulletin and Xenforo can (the other two platforms I use).
I agree that it is very useful feature - not only can it be used for users contacting staff or leaving private feedback but even for things like placing Topics in a moderation queue if they do not contain enough info or the mods need to question something about it (eg suspicious links, etc).