Why doesn't water in an open pan boil in a hot oven?

It will if you wait longer. Didn’t you ever made a casserole or something and have it bubbling when you take it out.

It takes longer because it’s not on direct heat like it is using the a burner on the stove top.

“It got to about 202 degrees F. but not to 212.”

You answered your own question there.

Because water boiling is the result of the hottest water in the container making the transition from water to steam, which takes additional energy beyond what it would take that mass of water go up a degree. There’s not enough additional energy in the heat of the air to get the 212 degrees F water to turn into steam.