I remember doing a demo at an LV seminar that included cutting out some 2" wood with a bandsaw. I was trying to hold the line, because in the particular case, the grippyness of the rough cut was going to be the final surface, so it needed it to be as flat as possible. I got some "ahhs" out of that one, and it did surprise me as I didn't think anything much about that kind of thing. As with all machine tools you can maintain a relatively quiet body; you have both hands to work with (well here is hoping anyway); the machine does all the work, what's the biggie.
About 20 years ago I got a new Laguna bandsaw in replacement for the chinese one I had. Carter guides, the whole 9 yards. I bought a bunch of their blades also. Wiggles like it's taking nips from a bottle when I am not looking. Never follows a line. I should shoot it, but instead I found an INCA I am restoring, and hope it will do better work.
One thing I do to follow a line is I place the square corner of the advancing kerf, on the line. I don't track the blade against the line.
I used to cut dovetail socket endgrain with a router when I started 35 years ago. I use a small bit, and climb cut for better control. The principle can be applied to other freehand routing, like doing inlay on guitars.