In olden times giving birth was 2.5 times as dangerous as going into battle.
Widowers were quite common.
Re-marriage was also quite common.
A widower who was also a father would likely re-marry and have more children by the next wife.
Or a father with one living wife might also marry another wife and have children by her.
So agnate half-siblings were pretty common.
Or a widow who was also a mother might remarry and have more children by the second husband.
So enate or uterine half-siblings were pretty common too.
And a widower who was a father might marry a widow who was a mother. That happened in Cinderella, for instance. So step-siblings were also quite common.
I suppose a father whose first wife was still living with him, might marry a widowed mother; maybe because she was his brother’s widow, or because of something like what happened to the Mormons in the 19th century.
Whether you want these relationships in the “core” vocabulary, may depend on something else than how common they are. But if there’s an obstacle, lack of commonness isn’t it.