The evidence for mobility is limited, as is the mobility, and where it has occurred has been the consequence of specific events within specific societies. Dickens went from a poor background (was it really that deprived?) but his advance was largely due to publication changes and the greater popularity of English because of colonialism, particularly in Asia and America. Mass publication provided by greater education (same with Shakespeare) resulted in expanded economies.
But much of the present concepts of business and wealth mobility (my phrase is meant) arrived from changes in Victorian UK and concepts of business in the US, which occasioned the gilded age involving a rich caste separate from the general population. In US this enhanced aristocracy represented the Gilded Age where money was inherited. Trump and Musk are marked examples and politically dominate the technocrates, the owners of Amazon and Facebook. Inherited wealth dominates wealth castes.