When braising, how deep should I fill a single pot?

Mark Bittman's recipe for chicken Adobo says: "Combine the [ingredients] in a covered skillet or saucepan large enough to hold the chicken in one layer". The recipe calls for 3-4 pounds of chicken.

I'm wondering what is the reason that the chicken must fit in one layer. Is it to ensure that the cooking temperature does not vary too much from the bottom of the pot to the top?

I'm also wondering in general, for most recipes that involve stovetop cooking in liquid like braises, stews, chili, arroz con pollo, etc., is there a limit to how deep I should pile it in one pot? when it exceeds a certain depth, should I split it in 2 pots?

Extra info: My biggest cooking pot is 5.5 inches deep, has a 10 inch diameter, and has a fairly thick base. My stovetop has gas burners.