It doesn't need to be literal random in "randomise your subclass" sense, merely that the character build options are such that the character can organically grow and branch into different directions depending on what makes most sense in the emerging narrative, instead of it all being preplanned from the get go.
And that's a good thing - but it shouldn't preclude players having enough control to feel like it's the character they wanted to play.
Which is a tough balance to strike.
A better, pithier response I could not make.
I get wanting organic character growth; I do. But every system I've seen for actually
making organic character growth tends to produce...well, the kind of stuff that came out of 3e. Skill points were supposed to let you invest in whatever you wanted, and instead ended up being really punishing and meticulous. Feats (in 3e) were supposed to feel like chunky blocks of cool stuff, and instead were either fiddly-nothing (or
worse), or overwhelmingly powerful and (almost) ne'er the twain shall meet. The two systems specifically intended to encourage variety ended up punishing it instead. Ability scores are at risk of the same, e.g. in 3e you'd rarely see an Int 18 Fighter and
never an Int 8 Wizard, the former because they have no use for such high Int apart from skill points, the latter because the game
forbids a Wizard from casting spells if they don't have at least 10+spell level Intelligence (meaning an Int 9 or lower Wizard cannot even cast cantrips--and every Wizard worth their salt always aims for at least Int 19 to be able to cast 9th level spells--preferably Int 20.)
It really is an extremely difficult design issue. Keep things loose and open, and people are quite likely to feel punished (whether or not that feeling is accurate or appropriate) for not measuring up. Keep things tight and focused, and people (such as yourself) feel it's "preplanned from the get go." Several middle-of-the-road options have failed miserably, making the situation worse in both directions (heightening the feeling of "punishment" for "falling behind" AND the feeling that things need to be preplanned.)
Personally, I think you are over-reacting at least a little to the existence of classes with levels. Like...that's what having "a class" IS, mechanically. It's something where you can see where it goes going forward, a collection of elements. By fogging, or randomizing, or making vague those things, you are directly disrupting the class-based design of the game. If "organic" growth is what you want, classes will never truly fulfill that desire, you will always be compromising on it to some degree.
It is? That's news to me. People rather play up the fact that Barbarian is one of exactly three classes (it, Fighter, and Rogue) that aren't innately magical to some degree in 5e. Monk ki is magical, and every other class has spells. Rage is one of the few explicitly
non-magical class features.