What is the importance of the coefficients in a balanced chemical reaction?
What is the importance of counting your change when you make a cash transaction with a large denomination bank-note?
Chemical reactions conserve mass. If 10 g of reactant are used in a chemical reaction, at most we can get 10 g of product. In practice we are not even going to get that, because losses always occur on handling.
When a chemical reaction is written, the stoichiometry must reflect the mass balance, which is absolute. Garbage out must equal garbage in. And of course we use the coefficients to depict that stoichiometry. The coefficients allow chemists to count their change effectively.