Oil pump hell.

Sterling said
Could have good compression, and bad oil rings, so it runs good but smokes. Could also have intake and head mismatch, sucking oil from the valley.

And or about 10 other things.:D
I went to sell a Coronet that smoked starting about 2 minuets after fire up and smoke like a pig for about 10.
The valve cover gaskets were seeping down between the heads and manifold and getting the inside of the manifold wet.
There are actually a lot of possibilities is the point.

RustyRatRod said
Indeed you have, but it's a myth.

Especially with modern thinner oils like synthetics for example.