That, however, is not Falstaff’s only role.
He is also a foil in Shakespeare’s sarcastic commentary about general corruption (Henry IV Part 2). That is not directly related to his relationship with Prince Hal. The point of that bit is how the system lets Falstaff get away with his shenanigans. Like recruiting Mouldy, Shadow, Wart, Feeble and Bullcalf, and getting paid to do so.
Shakespeare loved Falstaff. He is the only character he used in three plays.
You are 15x more well read than I am. All I knew about Falstaff was that he drank and was a jolly man.