You are right that cooling will be worse then heating.
your returns are to small( 16" = 1000 cfm flex)12"= 500 cfm
flex duct. 5 tons = 2000 cfm. thats one part of it. The grill size ( 2 cfm per 1sq inch of return area. 2000/2 = 1000 sq " a 20x25= 500 2 pc.
the noise of the grill is due to to much air trying to get by the small grill. they could install commercial style wide faced grill. tell them to check static syste pressure.

Last week I got a new furnace. There was a whistle/whine/moan that drove me bonkers. They came back out, went into my attic twice, ran new ductwork, taped things. The noise got worse, accentuated in my hallway. Meanwhile, I researched the harmonics issue online and most people pointed to the return grille. Mine had the gill-type louvers. People suggested turning it 180 degrees, while others suggested an egg-crate grille. The heater people returned today and said, we think it might be your return grille! I resisted saying, I knew it!!! The minute the old one came off...silence. Now I have a nice egg-crate grill and everyone is happy. I'm not sure why they didn't think of that immediately, but all's well that ends well.

Your ducts are too small but I find that the whistles are usually the grill or filter. You can change out grill styles and filter if applicable. But your ducts are still too small.

Mostly they are going to suggest changing the filter/grill and it will help. I don't know if this strategy is common place. That is - install everything undersized - create noises - come back with a fix. Then you are happy it is better when it still isn't right. People then feel satisfied and don't want to be too picky. I think it is a good strategy for making customers satisfied while putting in inadequate systems.

Your duct work would not pass code in my area.