According to statistical theory if it's not significant it's likely 0.
That is absolutely not what the theory says. First of all, effects of any variable are never really 0. They may be imperceptibly small, perhaps too small for instrumentation to detect, but never actually 0.
Second of all, the theory when properly interpreted really says that when the p value is greater than 0.05 (let's call it $p$), then there is a $p$ probability that we observe effects at least as large of not larger assuming the effect was truly 0 and all of our assumptions about the data generating process associated with the test, possibly including but not limited to: Normality, independence, heterogeneity of variance, asymptotics, etc. That is very different from what you've said.
Third of all, including or excluding a variable has little to do with significance as I explain here.