There's no need to be this vague about it. If you order a certain number of things a year from Amazon, Prime pays for itself. If you don't, it doesn't.
You're greatly over-simplifying: why does Amazon even offer Prime? Because they know that if you have it, you're significantly more likely to order more stuff than you would have otherwise.
We we became parents, we took everyone's advice and did the three months of free Prime, to give ourselves hassle-free diapers, wipes, cat food, and all those other things that are nice to get delivered when you have a 2-month-old. But we quickly realized we were buying more things than we needed, and buying more things on a sudden whim than we would have normally. We let the trial offer expire.
So don't compare the price to just the cost of shipping what you need -- add to that the cost of all the stuff you'll buy that you didn't need. If that still sounds good, then getting Prime is great.