What do you mean by "barely" respecting robots.txt? Wouldn't that be more binary? Are they respecting some directives and ignoring others?
That counts as barely imho.
I found this out after OpenAI was decimating my site and ignoring the wildcard deny all. I had to add entires specifically for their three bots to get them to stop.
there is a case to be made about the value of the traffic you'll get from oai search though...
And how often does it check robots.txt? ClaudeBot will make hundreds of thousands of requests before it re-checks robots.txt to see that you asked it to please stop DDoSing you.
New reason preventing your pages from being indexed
Search Console has identified that some pages on your site are not being indexed
due to the following new reason:
Indexed, though blocked by robots.txt
If this reason is not intentional, we recommend that you fix it in order to get
affected pages indexed and appearing on Google.
Open indexing report
Message type: [WNC-20237597]