Without interaction terms in a model, coefficients of lower order terms represents partial regression weights (i.e. how much influence does one parameter have assuming all other parameters are held constant). With interaction terms in a model, these same coefficients now represents conditional regression weights (i.e. how much influence does one parameter have when all other parameters are zero) and interaction terms* represent how much does one parameter's influence change when the value of another parameter changes. (Citation)

This means that by including interaction terms you lose the partial regression weights. Is there ever a situation where I can justify not including interaction terms by saying 'I wanted to know how much influence a parameter had when all other parameters where held constant, so I had to exclude the interaction terms'?

*This is the interpretation for second degree interaction terms, but my question does not change if you include higher degree interaction terms.

Without interaction terms in a model, coefficients of lower order terms represents partial regression weights (i.e. how much influence does one parameter have assuming all other parameters are held constant). With interaction terms in a model, these same coefficients now represents conditional regression weights (i.e. how much influence does one parameter have when all other parameters are zero) and interaction terms* represent how much does one parameter's influence change when the value of another parameter changes. (Citation)

This means that by including interaction terms you lose the partial regression weights. Is there ever a situation where I can justify not including interaction terms by saying 'I wanted to know how much influence a parameter had when all other parameters where held constant, so I had to exclude the interaction terms'?

*This is the interpretation for second degree interaction terms, but my question does not change if you include higher degree interaction terms.

Edit to provide example: Lets say you have enough data to make a linear model where the parameters are a bunch of characteristics of female wolves and the response is fitness. Three of these parameters are how dark the wolves' coat is (C), the weight above the average (W), and the age of the wolves (A). You have three wolves available to you; a male and 2 females. The females are the same age, but one has a darker coat and the other is larger. If presented with both females, which will the male prefer?

If you do not include interaction terms, this is a simple question to answer. A is constant, so if C has a larger coefficient than W than the darker wolf should be selected, and if the coefficient of W is larger than the reverse should happen. In other words, if the benefit gained by a dark coat is greater than the benefit gained by having a larger mother, than the male should pick the darker wolf, and the reverse should happen if the benefits are reversed.

If you include interaction terms, I do not see how you can answer the question. The coefficients of C and W only mean something if all other parameters are 0, which they are not in this case. The interaction term CxW tells you how the influence of C changes if W changes or vice versa, but that is irrelevant to the question you are asking.