I would not presume to tell you how you "should" run your business.
But yes you certainly could get some advantages to doing it that way
By keeping track of inventory you will know how much you are spending on what and how quickly and how much is available at any given time
What you probably want to do is incorporate it into job costing.
You purchase so much of each item and when your ccontractors pick up the material it is assigned to a particular job
that tells you how much you are spending on each job and how much material it used.
At some point you might draw the line and say its just not worth tracking this item. It cost too little to bother with and we will just put it all down to overhead and buy more whenever it looks like its running low. But for any item the amount of which is known for a job and factored into the cost and especially if it is factored into the price, it is helpful to know that you have enough on hand and the proper amount was used in the job.
this page has some basic instructions on how to set it up and use it
This is an hour long video on how people are using it if you want to watch