Looking at the characters we do know from canon i'd say it's only the last generation where basically all the clans heirs "happened" to be in the same class that screws our perception.
If you look beyond the main cast there's a LOT of characters who we basically have no information about their family beyond the fact that they are not from the usual main clans. Yugao, ibiki, ebisu, genma, hayate, kabuto, anko, just to name a few... Pretty sure Might Dai/Guy also count as non-clan ninjas.
Heck, of the advisers of the Hokage, iirc only Danzo is from a clan.
As far as i know the exhaustive list of ninja clans in Konoha is :
Aburame, Akimichi, Hatake, Hyuga, Inuzaka, Kurama, Nara, Sarutobi, Senju, Shimura, Uchiha, Uzumaki & Yamanaka.
I believe the "Lee" Clan is basically created by bushy-brows himself, so it hardly counts.
As i see it non-clan ninjas make the vast majority of the numbers, where as clan ninjas are of higher quality*. So they are the ones that usually end up in charge.
Just take a look at the family tree of the clan ninja we know... i don't remember a single case of three siblings. There's a few clan ninjas that have a pair of children but most are single childs...
* mostly due to better earlier training. ie: Sasuke basically entered the academy with a chunin level fire jutsu...
A civilian ninja basically has no training beyond the academy (and whatever his jounin sensei gives him, which... considering the four we know usually isn't much).
A non-clan ninja born out of ninja parent(s) will have some extra training from his parent(s) assuming s/he is/are alive and preferably not crippled (which is not a given), but that only offers decent training in whatever specialty the parent(s) has.
A clan ninja will have not only surrogate parents in case his are dead, but also multi-generational training available in most of the ninja specialties and ,on top of that, usually exclusive clan secret jutsu/bloodline.
As i see it, on average, a civilian is expected to end his career as a genin, maybe chunin if he's lucky and talented.
A non-clan ninja is expected to stumble up until chunin/special Jounin.
And a clan Ninja is fully expected to end up as a Jounin ninja if he doesn't get killed too soon.
Respectively fodder, specialists and leaders.