I started a new student today, a teenager with some talent, but limited time and only moderate patience for really digging into technique.
In any skill-based endeavor, technique is crucial, but sometimes I think it's okay to do something badly, that is, to not push through to be the best at some given thing. For instance, I love to cook, and I'm pretty good at it, but I've never felt like I need to have the technical skills of a chef, or to know the chemistry behind it, or be able to wield a knife like the sushi chef at Kamehachi.
So you can take skating with a grain of salt, and a toe-push or two as well. I asked my student whether she wanted to learn really great technique, or if she just wanted to learn tricks. She knew just what I meant, and told me she wanted to be able to do jumps and spins. Now, her technique is a little sketchy; her turns are clunky, and her edges wobbly. But her basic skating has a nice flow and she's motivated by her desire to jump. So I told her we would focus on skills, but that she needs to understand there are some techniques that you cannot skip, and some of them can be tedious to drill and to learn.
Each skater (and their parents) need to know what they want to get out of the sport. This can change-- I've seen skaters who started out just wanting "to skate backwards" go on to USFS testing and competitions, and I've seen high test competitive skaters turn recreational. But each time you get on the ice, you should understand where it is you're going right now. This is especially crucial for parents, whose goals may be different from the child's, sometimes out of ego, but sometimes just out of the fact that adults have a longer "dream" arc-- they can see the 16-year old doing triples in the 8-year old who just wants to skate with her friends. Both goals are correct, but they are not necessarily the same goal. They might be-- I've seen a lot of kids motivated by the idea of keeping up with their friends, too. But, again, that's a slightly different outlook from "win competitions." It might lead to that outcome, but the path is not the same.
A lot of coaches push for more serious skating than kids or parents are ready for as well. Sometimes the coach is thinking about her own investment. Securing a private student is time consuming. If that student doesn't get really into it, they might leave, and then you have to replace them. This, of course, is self-defeating. If I'm teaching the student what I need, that student will feel pressured and unfulfilled and will leave anyway. Coaches push kids into tests or competitions from ego, just as parents, and even skaters do.
Conversely, there are coaches who are emphatically not "competitive" coaches. I had a competitive daughter who moved to a coach who didn't do competitions. We didn't believe her when we switched, but guess what? She didn't do a competition with that coach until 5 years of coaching had gone by. That coach didn't do competitions.
Sometimes a coach will decide they're a certain "kind" of coach-- "competitive," "serious," "recreational" etc. And rather than refusing a student who doesn't fit that mold, they try to mold the skater into "their kind" of student. An ethical coach will ask you what your current goals are, and will let you know if this is compatible with the coach's goals and methods. Don't count on a coach to teach your student differently.
Long story short, know what you want. Know what your child wants (that's what really counts). And find out what coach is going to honor that.