I press open almost all the time, and I personally believe the "to the side" is a leftover from hand sewing and from times when thinks like electric irons were not available. About the only time I don't is when doing curved seams like with Grandmother's Fan or Drunkard's Path.
Is a personal decision, but I think pressing open is/will be more popular with the machine quilting we have nowadays. I should mention that I find it necessary/helpful to use a small needle (typically I piece with a 10) and a small stitch length. I'm not sure how the newer machines measure stitches, but I use a 1.85-1.90 on my Bernina and not the 2.5 it defaults to when turning on. Open pressing or not, I feel the small stitches are good/required any time you are doing modern strip piecing techniques and sub-cutting through previous rounds of stitching.
For some of my reasons for pressing open, I like having one rule to follow. Pressing to the side is generally press to the darker fabric, that isn't always possible when you are putting together two white pieces for example. And then there are other construction considerations on why/when not pressing to the dark side is used. Sure, it's cool when the seams twirl around, but (again) I use a small needle and a small stitch and don't want to take out any stitches at all (plus I can't really see them). I feel I am more accurate with my seams, being able to meet the seam and the seam allowances -- I also pin a lot, every leading seam edge or every 2". A lot of my friends get great results hardly pinning at all, but not me. BTW, when I pin I am pretty far down the seam allowance so my pins don't go under the 1/4" quilter's foot I usually use.
Some people feel that pressing seams open is more time consuming and fiddly than pressing them to the side -- I don't see a great deal of difference when I am sewing with my friends. I have learned things like I keep my sets of units chain pieced until after I press, the running thread helps keep the units in line. Also, while I don't use starch, why I insist on my fabric being nicely pressed and crisp is because it helps the seams stand up to be opened flat.
I also do a lot of "cut big and trim down" techniques. 20 or so years ago I was not very complimentary on what I then called "fabric wasteful techniques". I find the time I spent being very accurate is about the amount of time I spend trimming, and I get better results with trimming. Not all shapes and/or techniques work well because of geometry stuff, so no "one rule" to help me. Various shapes, however, do have their own rules. This week for the Bonnie Hunter Mystery we will have a "triangle in a square" block. In that case I cut the triangle as directed, but make the "skinny" side triangles larger and trim them down.