Depending on the machine used, sometimes a stump is left high so that a stump can have better leverage applied to it, In particular bulldozers; they get a better bite on stumps with a higher stump on it, and as RCBS points out, smaller sized machines with diggers. The exception is an excavator, as it has enough leverage without hooking onto the stump to rip it from the ground. Generally I like a higher stump if I am going to clear the land for fields just because a taller stump is easier to find when I am rooting around trying to remove them.
There is a little extra stump there for leverage with my excavator. The escape paths I get, but the snow was 2 ft deep and who knows what was under there. My botch was solid, but large. So using a wedge was virtually impossible. I like the idea of using the plunge cut method, which I will try out maybe this weekend.
I'll bet that whole ordeal was a "butt pucker". Have a bud that's a semi-driver...................he says that until you've had 3 "butt pucker" situations while driving; you've not been driving semis long enough.
Lots of good learning information here. Glad you were able to recognise the hazard and share how it went and how it could have gone wrong so quickly. Most people here are family men and women. Any injury or worse has a profound impact on the family. I swear that it was The Lord looking over me when I had my tree cutting days. Reading the postings here and elsewhere on this forum has shown me how really at risk I was. I learned by trial and error. No one to show me anything about cutting etc. I survived. Luck of the dumb I guess. I never took my sons out when I dropped a tree. They went out with experienced cutter when it was time for them to learn. They did help me with the splitting and stacking. So far, no one has been injured. I know accidents happen even to the experienced.