Maybe it didn't matter that much in Dynasty. Even in season 1, a loan depended on the marriage between Jeff and Fallon, another loan depended on Krystle's necklace, Alexis' affair with a sheik etc etc.
And even if you inherit the majority of the shares (I assume Cecil and Jeff weren't the only shareholders) then that doesn't automatically make you the CEO of that company, it only impacts the power of the voting rights.
Either way, they could have shown the preperations for her position i.e. being informed and advised by Jeff and all the heads of the various departments - not Adam because he's just a lawyer from Hicksville. He knows as much about oil as Alexis does.
And there were no board meetings (except for the power struggles), shareholder meetings, experts - there was nothing remotely realistic about Dynasty's business, although in season 1 it still kinda looked realistic.
But is that what the Dynasty viewers really wanted to see, especially since season 2 was revamped to show more glamour and bitchy intrigue?