Preheat the oven to 350 degrees F (175 degrees C). Grease three 8-inch cake pans.

Combine flour, sugar, salt, baking soda, and cinnamon in a large bowl. Beat in eggs, oil, and vanilla extract. Stir in bananas, pecans, and pineapple. Divide batter among the prepared pans.

Bake in the preheated oven until a toothpick inserted into the centers comes out clean, 25 to 30 minutes. Cool in the pans for 5 minutes. Invert onto wire racks and let cool completely.

Make frosting while cake layers are cooling. Combine cream cheese and butter in a bowl; beat with an electric mixer until creamy. Add powdered sugar and vanilla extract; mix until creamy.

Spread frosting onto the cooled cake layers. Stack layers; frost top and sides.