Not unreasonable by any means.
I approach all data on ESRI as open, even when owners/ESRI go out of their way to hide access to it.
No licensing on the page is unfortunate indeed. And no way to contact the government department behind the API directly just doubles down on the unfortunate.
When I'm snooping around the featureServer's and I have questions like this, I go to ESRI's open data hub and search for the user/group and/or dataset. Probably half of the time, the dataset from the featureServer API is also in use in the open data hub. If this is the case, there should (some user's do not fill in their data's metadata, etc.) be a data profile page representing that data, with relevant information, including usage and contact information.
So for your example, I searched for
ESRI open data, and clicked on the ESRI open data hub link in SERPs. Then I searched for
btd pavement in the ESRI hub, which provided this metadata profile page for btd/pavement markings which I think is exactly what you were seeking.
If you look at the links below the Layers header, they're all pointing to the featureServer's URLs for the dataset you are seeking.
You can also use the hub to search for similar data and/or data from same user/group, etc. I realize that is incredibly obvious, but still wanted to point out how much more data I've come across doing data stalking in this manner.
Lastly, when I do find featureServer's consisting of data I desire/need/want, almost all of the time, I use pyesridump, a lightweight python utility, to suck down the data, which gives me independence around what I would like to do with the data.