Our wood stove had a side-open door. As did our coal fire. In retrospect, they had heavy doors, and tough hinges, so part of the reason was that they could open sideways because of the hinges, and couldn’t open down because of the weight. Those doors were hot, and there was good clearance in all directions around the kitchen and around the fire.
Our oven door has struts, and complicated hinges, to stop it falling open, or falling when it’s opened, and is gradually failing, so whatever the reason it’s not because it’s mechanically better.
Refrigerator doors always seem to open on the wrong side, and block your view and access from one side, but allow you to reach deep inside the refrigerator. Comparing the experience, I’d say that
You don’t want to reach deep inside a home oven, pushing past the door – that’s how you get burned.
Access from the correct side is important – you don’t want to have to go to the wrong side to get something from the oven, then walk around the door.
You don’t want the door to hide the view of someone walking on the other side – you want to have a clear view of where you are going with the hot item.
All of these problems could be mitigated by having a bigger kitchen with fewer people in it.