TL;DR - I agree with the proposal
Note that I found it was rather difficult to formulate an answer to this question, without making it sound negative, opinionated and panic inducing. In fact I decided to remove quite a bit, and just leave in factual links and quotes.
I came across this meta question over on SO today, How can we determine whether an answer used ChatGPT?, and this answer in particular grabbed my attention:
I don't think there's going to be any value in having you, a mere mortal, try to determine if an answer or question was generated by ChatGPT.
The reason is super, super simple: we don't want this to turn into a witch hunt.
There are things you can do even today to help with curation of answers; if an answer is wrong or incomplete, you can downvote it. If you happen to notice a trend of similarly bad answers from an account, you can flag for moderator attention with the series of answers you've got as evidence.
This shouldn't be a "those bad answers are more moderatable than others" situation - just vote on answers as you always would, and let the moderators deal with the heavier lifting on this circumstance.
Which raises a valid point of allowing suspicion and doubt to get the better of us.
Yes, we have recently seen some questionable posts, and (to be frank) even now I am still not 100% convinced what the root cause of those posts were.
Nevertheless, community voting and flagging seem to allow us to handle such situations reasonably well.
However, one thing that is certain: ChatGPT, and any other derivatives, are not going to go away, and it is probably going to become more and more difficult, as time goes by and the technology "improves", to detect such posts.
The tools that you used (and refer to in your question), while I haven't tried them myself, look useful - even though they themselves would also appear to be using some sort of artificial decision making! The best tools are probably our own eyes and knowledge to root out suspect sentences and phrasing as well as (more importantly) suspect advice.
In addition, a couple of answers (to the linked to meta SO question) also point out some good tips and what to look for - such as this answer and the first paragraph of this answer, in particular.