I have tried to pursue this about as far as I think I could through the support channels. In the end I got a call back from a reasonable support agent, but I fear that in the end they are all fairly clueless. They had me take a photo of the screen first to demonstrate that there was no setting to turn off the screensaver, which they believed existed. So it looks like this was a setting, but has since been removed or doesn't get included on some models.
In the end, the problem is still here and we're no step closer to a solution, but I was assured my feedback would be passed on to the development team.
Some things I suggested if disabling the screensaver is too hard for them:
Allow us to configure the duration of the screensaver so it at least doesn't kick in after 2 minutes, but perhaps after 15 or 30 minutes only which would make it much less obnoxious.
Allow apps to override this so apps like Spotify can disable it
Show a warning that you disable the screensaver at your own risk of screen burn in but allow us to do it anyway
Allow us to disable it temporarily, e.g. for 24 hours, so we can use apps like Spotify or someone mentioned karaoke, without the screensaver kicking in, but for it to re-enable again after a day to continue "protecting" us from ourselves.
So many options to address this and make it less obnoxious, but unfortunately I don't think there's a way to get directly in touch with the development team to pass them such kind of feedback, so one can only hope they read forums like this.
I have gotten used to not being able to use the TV the way I want to now, and found some hacks to bypass the issue. For example, the screensaver doesn't kick in when you have media through HDMI coming in, so you can just use Spotify on a Chromecast unit instead.
But if this problem doesn't go away at some stage, my next tv will definitely not be LG.