yes they do.
but, your coach has to think about a lot of things other than your aerobic system. he has to consider that at 14 you are going through puberty, which may not feel like much to you but is incredibly stressfull on your system. he has to think about how much growing you still have to do. he has to think about your long term training future. he has to think about you finding time for other sports, and doing other 14-year-old boy stuff like climbing trees and skateboarding and building explosive devices in your friends garage etc, etc, etc.
so, yes, you're right. running easy miles is good for you. but your coach is right too. there needs to be time for things other than running.
this is not clever. if you do a long run on Saturday then Sunday is a rest day. always. just as easy runs are good for your aerobic system, rest days are good for every part of your body, ESPECIALLY after a long run. you need the rest to recover properly and to acquire the benefit of the training that you did. rest and recovery are important aspects of every training program. do not overlook this.
it's really hard being 14 because you are old enough to start making choices for yourself but you get all sorts of different advice and orders and instructions from folks, from teachers, from coaches, from your cub scout leader, from some random stranger on the internet and who knows where else. but ultimately, it's your life. you have to live with the consequences of your choices and those other folks do not.
my advice, for what it's worth, is, if you have built up to running easy for an hour on Saturdays, and you can keep doing this without it affecting the rest of your training, if you are recovering well and ripped and ready to go come practice days, then keep that up. don't feel that you have to do this every single Saturday, it's okay to take a down week every 3 - 4 weeks, shortening the run or missing it out altogether can be cool too. but this is a generally good thing to do. and it stops you building explosive devices in your friends garage if nothing else.
however, you should follow your coach's advice about not running on rest days. what I said about rest and recovery is important. if you really feel that you need to do more mileage, then you have two clever options. first, run a longer cool down on practice days. if you normally do a mile, or mile-and-a-half to cool down, you can extend this a bit and turn it into an easy 3 miler, but make sure it is easy. the second option is to do a short run in the morning before school on practice days.
cheers.