Hmmm... I can't reproduce that. I can move automation in a project with nothing but automation in it using that method. And I don't even have the automation specifically selected - all edit filters are set to clips.
 
Also, I just checked, and dragging is working as well - Select the time range, select all tracks, drag a MIDI clip that's in the selection, and the automation in the synth track goes with it.
 
I can't think offhand what settings or project state might cause it to not be working (other than nodes at the beginning of the track as mentioned earlier), but you should keep looking around and maybe try it in a test project. It should work.
 
 

One caveat regarding select by lasso:  Lasso only selects whatever is currently shown by the edit filter, so the automation won't be included if the edit filter is set to clips. You can do the initial selection by lasso, but then you need to Ctrl-click add the track with the automation to the selection. Selecting the time range and tracks separately avoids this.

sharke
New oddities: when I get the whole project in view and lasso everything, all of the clips within the lasso are selected except one which stays unselected. So much frustrate 
 

 
See my post above. If you're doing all your selecting by lasso, Edit Filter settings might explain all you issues. If you want to select everything in a project, you need to Select the time range and tracks directly or Ctrl-A and then select the time range.
 

All the edit filters are set to clips. There is no logical reason why lassoing everything would result in everything being selected except one random clip in the middle of the project. 
 
Things just get weirder. Here is a screenshot of the whole project. I've just lassoed everything. Note the relative positions of the clips within the red rectangle. 
 

 
I then dragged everything across to bar 1. Below is a screenshot of the result. Observe how after the drag, only some of the clips are selected (it seems to be random). Also note the same clips within the red rectangle - they are now positioned differently relative to each other than before the drag. It's like I've drag copied instead of dragged, and left some clips remaining. But all I did was drag, I didn't CTRL-drag anything. 

 
 
I'm just at a loss to work out what's going on here. These things are typical of the oddities that seem to build up in a project the longer I work on it. If this is expected behavior and there's some kind of functionality that I'm not getting, I'd like it explained. Otherwise I'm curious to know why such a simple task as selecting and dragging clips still doesn't work properly. 

Ok so here's some new information to add to this dragging oddity. It's clear from the images above that what's happened is that it's drag-copied the project instead of just moving it. Indeed when I recreate this action, I see that I'm getting the little + icon when I drag. I did not notice that before. I should not be getting that copy icon unless I have CTRL held down though, correct? I'm not holding CTRL down. 
 
But here's the weird part - this erroneous drag-copy behavior only happens if I drag the selection from a MIDI clip. If I drag it from an audio clip, the project moves as it should, without copying. Definitely something very buggy going on here.
 
More info: This unwanted drag-copy behavior only happens when I have both audio and MIDI clips selected. If I select everything but the audio clips, it drags without copying. If I select just the audio, it drags without copying. If I select both MIDI and audio AND I drag the selection from a MIDI clip, then the little + sign appears and it drag-copies. 

So I started a new project and inserted some random audio and MIDI tracks with clips in them, and tried to reproduce this behavior. It's not happening - I can select all audio and MIDI clips and drag them from a MIDI clip and they move without copying. Looks like this oddity is yet another case of a project steadily going screwy over time. I have projects from the past that I've abandoned because too much weird stuff like this started happening in them. And it always seems to be very basic stuff like moving clips around and copying. Think I'll send this project to Cake. 

does it depend on where on the clip you click, when you do the click -to-drag?

I'm dragging on the left hand side of the clip like I always do. And I'm grabbing the same part of the clip when I drag MIDI clips as when I drag audio clips, and yet both behave differently.

I think what lawp was alluding to is that in the X series, sometimes it matters whereabouts vertically in the clip you start the click & drag action.
 
Whether it makes any difference or not, I don't know

Bristol_Jonesey
I think what lawp was alluding to is that in the X series, sometimes it matters whereabouts vertically in the clip you start the click & drag action.
 
Whether it makes any difference or not, I don't know

Vertically speaking, the only place you can drag a clip from is the bar at the top. Here, the icon turns into that directional cross thingy. You cannot drag a clip from anywhere else. The horizontal position from where you drag is important though - if you do it from the left then you're going to be snapping the left side of the clip, and if you do it from the right then the right side snaps. As far as I know, there is no way to drag-copy a clip without holding down CTRL as you drag. And I definitely wasn't doing that.