I definitely think linear algebra has a lot of practical applications, but I'm not sure I would necessarily call it the "best" nor the "most valuable tool overa

I definitely think linear algebra has a lot of practical applications, but I'm not sure I would necessarily call it the "best" nor the "most valuable tool overall". It certainly provides the most bang for your buck if you are doing certain kinds of modeling, but even just within modeling which tool will be the most useful will depend a ton on what you are doing. For example, for dynamical systems you may be using linear algebra, but mostly as a computational tool for solving differential equations. In this case, analysis of your problem at the level of calculus is extremely important if you want to come up with an accurate and computationally feasible model.