>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](https://stats.stackexchange.com/questions/413606/when-to-remove-insignificant-variables/413609#413609).