Do successful french macarons really need precise weight measurements?

I can tell you that yes, every part of the process, including precise measurement, has really low error tolerance. Do something a bit wrong, and you end up with an edible cookie, which does not resemble a macaron in shape or texture.

My explanation for the different ratios you found is: the really important thing about the ratio is the final moisture content of the batter. Different recipes exist, because there are different ways to reach the same final batter moisture.

• both sugar and almonds bind moisture from the egg whites. So it isn't enough to look only at the almond:eggwhite ratio. The recipes with more almonds probably use less sugar, if the process is similar.
• the process itself matters a lot. Making an Italian, French or Swiss meringue will have an influence on the amount of liquid available for the almonds to absorb.
• almond flour does not have a standard moisture content. If a chef has his almonds cracked daily and processed into flour, they will absorb much less water than if he buys a pack of almond flour at the supermarket.
• aged eggwhites will behave slightly differently than unaged, some recipes will be written for aged eggwhites and other for fresh ones.
• finally, not every recipe out there is a good one. It's very possible that a few recipes from your sample will never produce a good macaron.

You are, of course, welcome to try it without the precision. Especially after you have mastered them, you can play around and see if a different recipe gives you a slighlty different texture which you prefer. But if you already have a recipe which is supposed to work, I'd avoid changing anything about it.