Our 16 year old son runs cross-country and has run both XC and track off and on for several years. As far as I know, none of his coaches have recommended protein shakes either in talks with the team or to him individually (he has a classic distance runner's build--thin, wiry, somewhat short--and could use some bulk). They do emphasize eating 'healthy,' namely staying away from fast food and high-sugar, low nutrient foods. I'm sharing this point not to say that your son's coach is wrong, but rather to show that there are different philosophies out there. I'm no expert at all, however I would agree with you that if your son is getting plenty of protein now and he is performing well (running races faster as the season has progressed and reducing his mile time), there's no reason to change his diet. If it ain't broke, don't fix it!
That said, I have a couple thoughts on nutrition for these really active kids. You expressed concern about the protein bars because they have lots of sugar. That is true, however isn't that combination of sugar (quick energy), whole grains, protein, and fat is exactly what their bodies need when they are heading into an activity or recovering from one? If they're just sitting around the house, then the protein bars are not appropriate nutritionally, and indeed it's better for kids to develop the habit of eating real food, however my point is that protein bars may have their place in nourishing an active teen. Also, I will say that my kids have become very fond of smoothies in the past year, and they might be a useful addition to your kids' diet. I invested in an immersion blender and make various combinations of frozen fruit, plain yogurt, orange juice, avocado, frozen bananas, spinach, etc; everyone gobbles them up. If you want to try out the protein shake approach, it is possible to make protein shakes at home (I found LOTS of recipes on the web just now), and that way, you can adjust the sugar content to fit your kid's tastes. They seemed to involve purchased whey powder or protein powder, which gives you less control over the amount of sugar or other ingredients, but at least you can influence most of what goes into the shake more than if you buy them ready made. Anyway, good luck with it! I have become a big fan of cross-country as a sport and community. I hope your family has a great time with it.