This is tangential to your point, but every time I see an implication that Smith had anything in common with a modern conservative I feel the need to point out that not only did he not believe in inheritance as you said; he also believed in social welfare programs like public education, and anything else that the market would predictably not be able to handle. In his time healthcare was only starting to get to the point of realizing that cowpox was a useful innoculation for chickenpox, but I have no doubt he would believe in socialized healthcare in a modern context.

Smiths free market was never supposed to be this free:

Wherever there is great property there is great inequality. For one very rich man, there must be at least five hundred poor, and the affluence of the few supposes the indigence of the many. The affluence of the rich excites the indignation of the poor, who are often both driven by want, and prompted by envy, to invade his possessions.’    

Wealth of Nations, V:I.b, p.709-710

Civil government, so far as it is instituted for the security of property, is in reality instituted for the defence of the rich against the poor, or of those who have some property against those who have none at all.’    

Wealth of Nations, V:I.b, p.715

‘Corn is a necessary, silver is only a superfluity.’    

Wealth of Nations, I:XI.e, p.210

This disposition to admire, and almost to worship, the rich and the powerful, and to despise, or, at least, to neglect persons of poor and mean condition … is … the great and most universal cause of the corruption of our moral sentiments.’

Theory of Moral Sentiments, I:III, p.61

‘It must always be remembered, however, that it is the luxurious and not the necessary expense of the inferior ranks of people that ought ever to be taxed.’    

Wealth of Nations, V:II.h, p.888

‘The necessaries of life occasion the great expence of the poor. They find it difficult to get food, and the greater part of their little revenue is spent in getting it. The luxuries and vanities of life occasion the principal expense of the rich; and a magnificent house embellishes and sets off to the best advantage all the other luxuries and vanities which they possess … It is not very unreasonable that the rich should contribute to the publick expence, not only in proportion to their revenue, but something more than in that proportion.’    

Wealth of Nations, V:II.e, p.842