Of course you can. We even had a practical example in Syrian Kurdistan for several years in a row. Unfortunately, Rojava was destroyed by the Turkish invasion… It looks like the only thing you can't really do without some kind one central planning is war. Which would explain why every anarchist attempt have been crushed so far.
> when capitalism had reached its highest stage of development, and then the "transition" into socialism would be relatively natural and painless.
Natural (and according to Marx, it wasn't “relatively natural” but more like the obvious course of history) but in no way painless. Revolution and temporary dictatorship was part of Marx vision all along.
Also their is plenty of non-Marxist socialism, some being older than Marx and some modern.
> that would mean keeping all their eggs in one basket!
That may be an irrational choice, but humans do put all their eggs in one basket all the time! And BTW, this popular saying isn't that insightful: if you cannot afford to lose a single egg, you better put them in a single basket, because the probability of one basket failing is lower than multiple baskets ;).