On commodities and the carry trade – understanding the 'insurance premium' aspect

Been trying to get a handle on the nuances of commodity futures pricing, especially in relation to the carry trade. I understand contango and backwardation in the usual supply/demand context. What I'm still trying to square away is the idea that sometimes, even if the expectation is for spot prices to rise, the futures curve might still show contango due to the 'insurance premium' or convenience yield aspects – basically, the cost of not having the physical commodity now.

For those of you trading the futures on, say, crude ($WTI, $BRN) or even some agricultural products, how much weight do you actually give to this 'insurance' component when assessing a potential long-term futures position? Is it something you explicitly model, or is it more of an underlying assumption that just shapes the general curve you're looking at? It feels like it could significantly impact returns if you're holding contracts for extended periods, and I'm curious how seasoned traders factor it in beyond just observing the term structure.