Golde is the perfect yin to Tevye's yang. He is given to flights of fancy, to quoting at length from midrash and scripture, and to building castles in the clouds imagining himself as a wealthy and very important man.
And her job? To be Marge Simpson, partly bringing him back down to earth and partly just straight up raining on his parade. Like this:
Oh, enough with the Torah, Tevye! Everybody knows you're a man of the Torah. Listen to me, your wife. (4.6-8)
Who cares about a midrash?" she says. "We have a daughter to marry off, and after that daughter, kayn eyn horeh, there are two more, and after the two—three more, may no evil eye befall them! (5.3)
This is straight-up sitcom material: the long-suffering wife and the doltish husband who still manages to get away with everything. She's probably even thin and pretty.
But notice that it still doesn't seem much like Golde is her own character. She never seems to get her way, and she basically hangs around to play the straight man to Tevye's comedian. Yeah, he's sad when she dies. But it'd be even nicer if he'd seemed to appreciate her as much when she was alive.