I don't think linear systems are any more prone to over-relying on random chance than non-linear ones - if you're using a random generator, you're using a random generator. Whether they produce a lot of failed results or not (or crits, fumbles, or successes) depends on the target numbers being set, not the fact that a random generator is involved.
Sure, you could make a game where the skill values overpower the RNG in most cases. Just taking some numbers off the top of my head, you could have a system where a novice has a skill value of like 10, a master has 50, and you roll d10+skill to see if you succeed. Maybe even an exploding d10 to reflect that you might accidentally luck into doing the right thing. This would provide a fairly narrow window of difficulties where random chance determines if you succeed or not, but in most cases you'd know ahead of time if you're good enough.
Bell curves accomplish a watered down version of this. Let's say we're playing GURPS (3d6, roll under or equal to skill) and you have skill 13 and I have 15. On a normal task, your chance is about 84% and mine is about 91%. We're both pretty good at our stuff and fairly likely to succeed. But let's say the task is difficult and has a -4 penalty. Now you're down to 37% and I'm at 62%. I'm still not
certain to succeed, but my higher skill helps me absorb more of the increased difficulty. Now, I'm not saying GURPS has the perfect skill system – far from it, the skills are too narrow, the costs are too high, and it's far too generous with penalties for everything. But that particular bit is pretty nice in reflecting how high skill has diminishing returns on normal tasks but is very helpful when things get difficult.
I think I've mentioned it before but I'd have loved to see a version of Pathfinder 2 where proficiency level (trained, expert, master, legendary) gates automatic success rather than allowing the attempt in the first place. They do have the Assurance skill feat you can take, but since that only counts proficiency bonus and not stats, items, and other buffs it's about equal to guaranteeing rolling a 5 or so.