There is a VERY good reason. BECAUSE NaCl is sodium chloride. Not NaCl2, Na2Cl, NaCl3 or any other arrangement. NaCl is the ONLY one that is a 1:1 ratio. Balancing equations would be SO MUCH easier if we could change subscripts BUT then you have changed the reactant or the product and only NaCl is NaCl.
NaCl + Pb(NO3)2 ==> PbCl2 + NaNO3.
So what you want to do is to rewrite this as
NaCl + PbNO3 ==> PbCl + NaNO3.
Easy, huh? BUT PbNO3 is NOT lead nitrate and PbCl is NOT lead chloride. In fact, PbNO3 and PbCl do not exist.
Regarding changing coefficients, we can change coefficients because we are simply saying we have twice as many or three times as many or any times as many; for example, 2NaCl instead of 1NaCl or we have 3AgCl instead of 1AgCl. Look at it this way. We go into a grocery store to buy jelly + bread + banana. Now we can buy 2 jars of jelly, 3 loaves of bread and 5 bananas and we haven't changed what we went to the store to purchase. BUT, if instead of this I purchase 1 lb of hamburger, a loaf of bread and a banana, I have changed the shopping list and my family will be mad at me, especially if they wanted a jelly/bread/banana sandwich. They aren't likely to like a hamburger, bread, and banana sandwich. In the first case (changing coefficients), my family can make more jelly/bread/banana sandwiches but if I change the shopping list they can't make any sandwiches.