The DM controls the spotlight. You can ensure that everyone has the opportunity to participate more or less equally over the course of a session, adventure, or campaign. Players can (and in my opinion should) also make sure their fellow players get as much screen time as they do. That's just good-spirited play in my view.
And on that note, the characters aren't competing with each other anyway. It's a good thing if someone on my team is great at what they do, even if I'm not as good at that same thing. Perhaps I'm good at other things or in other ways. Maybe I have to spend some extra resources like Inspiration from time to time to be as good or better. Perhaps I need to improve my player skill by striking a balance between relying on my character's bonuses and abilities and paying attention to the game and coming up with good approaches to goals that obviates the need to roll in the first place. That's a fun creative challenge in my view. If I'm not good at that sort of thing, the only way I'm going to get better at it is to do it. And why wouldn't I be up for trying to learn something new or improve my skill?
I see the game you propose as a thing full of opportunities, not rife with problems. Luck is not something one can control, but it can be mitigated with skillful play. And if I have a character that lacks in areas where my teammates do not, my fellow adventurers can pick up the slack, plus it will be that much sweeter when I succeed. So yeah, as DM, just make sure the spotlight falls more or less evenly on each player and character, talk to your players about what I say above, and I bet everything goes just fine.