In Lefkowitz v. Great Minneapolis Surplus Store, what is the reasoning or public policy for classifying normal advertisements as invitations to offer as opposed to being actual offers? What would happen if all advertisements were deemed offers?

The reasoning behind this practice is to give the sellers a bit more choice and power in the deal. When their advertisements are strictly offers, they are obligated to sell at the listed price without any leeway. However, changing the definition so that these advertisements become “invitations to offer” aids them by giving them some negotiable room.
An invitation to offer implies the seller does not have to accept the offer from any particular buyer and also leaves room for stipulations, should the seller choose to add them. By incorporating these aspects, the seller can choose to deny a sale under any pretense they wish. This gives them some power in the negotiation, instead of holding them to the terms of the initial advertisement.