"Would it work" sounds like you are on the same team as the other party and trying to concede something with them. I think that's why it's received better than

"Would it work" sounds like you are on the same team as the other party and trying to concede something with them. I think that's why it's received better than "Why not" which sounds like you are surprised and don't understand why the other party doesn't want to use your solution or worse it suggests that you think the other party is stupid and it's not understandable why they use another solution but you are sill trying not to say it out loud in suggesting the good solution. Pretty sure there are subtle differences between speakers of different languages once English is translated/understood.