Do you read journals, or "use a database"?

We had a reception for the Chemical Information Division of the American Chemical Society last night and I spent a considerable time talking with several staff in the publications side of the Society. (I am not attributing personal views in this post, just general impressions). It was illuminating. I'll try to be objective (it was a party and the drinks were provided by CAS). I met with the staff who were on the other side of our removal of service of ACS journals that I reported last week. Here are some thoughts…
There has been a major shift in how (some) Scientific Publishers see the purpose and practice of scholarly communication. Listening to the words used, "database" has replaced "journal" and "users" has replaced "readers". I suspect the latter word conflates "purchasing officers" with "readers" into an unhappy anonymous entity. Moreover there is a tension between the publisher and the users – significant content is illegally downloaded and an important role of the publisher is acting as "policeman" making sure that content is not stolen. Thus our problem last week was a student using Firefox and not understanding (realistically how could he?) that "open all tabs in browser" would put the University of Cambridge in breach of contract. Technically this may be true; however in police-community interactions overzealousness is not always a good strategy.  We parted with the observation the "Firefox is a problem".
Now, I have never advocated breaking or abolishing copyright, but it is clear that this is creating a tension in the publisher/reader community. I've been involved in setting or being on the board of scientific journals and I see their major purpose as enhancing scholarly communication. I'm worried that we are losing sight of this, where journals in non-profit organisations are seen as a way of subsiding other activities of the society. If the publishers see "users" as a group who have a major motive to steal content, I suspect things will get worse.
At some stage we seem to have flipped from a community where publishers interpreted the wishes of the community and served them – for a reasonable fee – to a world where publishers make the rules and police their non-compliance. Did anyone in the reader community:

• actually ask for journals to be transformed to databases?
• actually ask for content to be limited in time to the duration of a subscription (we used to have physical journals we could take home and even hand down to our descendants or give to needy institutions)

It worries me that this has happened almost silently. I remember in ca. 1970 (when I was too inexperienced to notice) that authors were asked to transfer copyright to publishers. These requests came from trusted societies – national societies and international unions  (At that stage there were essentially no commercial publishers – Pergamon was a few years later). I didn't think twice about it – but it was one of the biggest mistakes of my scientific life. Are we sleepwalking into something just as serious?
Objectively I have some sympathy with publishers whose content is illegally downloaded – I do believe in copyright. But pragmatically is the way forward to be increasingly draconian with readers (sorry, users)?