In tech, we call it premature optimisation.
Suppose recycling used more energy than it saved (which is the case for some materials e.g. low grade plastic waste in places with little plastic manufacturing). Then, even if that waste were most of the waste stream, getting people to recycle would not be essential-- it would actually create more waste, something to avoid.
My claim is that as long as recycling is a net gain, after you count all the costs, it doesn't matter what percentage of the total waste stream it is.
Note that I'm not saying that industry shouldn't also recycle. I suspect that the potential gains there are even larger, but that's not an argument against household recycling, given that the tasks are executed by different people in parallel.
Then you are ignoring the very existence of opportunity cost.
This is why unbiased figures are important. It's all relative. Why should everybody in my country have multiple bins picked up at different dates and have to separate garbage manually only to have a second group of people sort through it, if the overall effect is so tiny?