Ignore stuff if you don't want to be at your best. Ignoring avenues to improvement is a great way to not be at your best. Since this kid wants to be elite he should do everything he can, just doing more mileage and some core work isn't gonna get him to be the best runner he can be. But yes, if he wants to see how much he can improve without really giving it his all then just raising mileage is the best single thing he can do, of course he could just get injured doing this and then mileage doesn't do anything for him.
I have only coached a couple friends/former teammates for a few months each, but both saw huge improvements in that short time without even including the weights/cross training that I mentioned above. The way I structure a full training block is this, and this is just in general since I know nothing about you or your training. You want to build up your aerobic base, transition it into a high-end aerobic capacity, transition that into a good anaerobic capacity, then for your goal race(s) you want to taper your mileage down a bit, just do some sprint/short workouts, and rest up for the race(s).
Phase 1:
This phase is assuming you are coming off some period of no running after a season. Just start easy running again. Start building up mileage back to whatever mileage you are used to doing, or more than you are used to if you are looking to increase mileage. Increase mileage however fast you feel comfortable doing it. All easy runs. Start throwing a few 75-100m strides in at the ends of runs at some point during this phase. At some point also start doing a weekly long run.
You can do one fairly light workout a week here if you want, just like an easy fartlek or tempo run.
Also during this phase you should start lifting to build your muscular strength. And, if you can, start doing some cross training to help increase the base you are building. You can pretty much do as much cross training as you like, in general the more the better, as long as it isn't exhausting you for your runs.
This phase can last as long as it takes you to build up your mileage.
Phase 2:
You should be at your goal mileage now. Make sure your body is handling the mileage okay. If something is hurting or you're feeling exhausted take an easy week. The occasional easy week can head off injuries. Anyway, start adding in a weekly tempo run and a weekly hill workout and continue doing your weekly long run. Try to do both long/steady and short/steep hills. Your tempo runs should probably start at like a 2 mile tempo workout where you're going at a comfortably fast pace, not close to race pace. And build up to doing longer tempo workouts. My favorite is 5k tempo run, about a 10 minute break, and another 5k tempo at the same pace - if you can't run the same pace for the second one then you are running too fast. Depending on how long you have until your races this phase might be a month or 2-3 months (a full year training plan 3 months would be appropriate). Oh, you can also mix some fartleks in here occasionally to take the place of some of the other workouts if you want.
Phase 3:
Once you feel you have strong endurance and feel good going at a strong pace for a long period of time, and feel good on hills, then you want to transition into doing distance-oriented track training. Stuff like mile repeats. And you can continue doing tempo runs. You should be able to pop out a very good 5k by the end of this phase. Do this for a few weeks to a couple months, depending on the length of time you have until goal races.
Phase 4:
Anaerobic conditioning. Here you start doing hard track work. This is the bread and butter of a mid-distance runner. If focusing on 5k XC you only need to do some of this and should spend a bit longer in the previous phase. If training for a mile you should do 2 months of this. Basically twice a week do intervals 200-800 meters. Doing 400m intervals is pretty standard, but mix it up so you aren't doing the exact same thing every workout. Your mileage might drop a little bit now because your workouts contain less mileage.
Phase 5:
Racing time. Time for you to peak over the last few weeks or month of your training as your goal race(s) approach. Decrease mileage, start focusing your workouts on more like a series 100-200m sprints. Should get yourself rested before any race.
That's a basic training block: build endurance -> build high-end aerobic capacity -> build anaerobic capacity -> build speed and peak for your races.