TL:DR the framers of the US constitution set out to correct what they saw as weaknesses in the British parliamentary system, and in doing so they created, perhaps somewhat inadvertently, a different kind of system that is now known as "Presidential".

It's worth unpacking what we mean when we say that the US has a "presidential system of government" and the UK has a "parliamentary system". If we compare the institutions created by the US constitution with those already existing in eighteenth-century Great Britain, we see many similarities:

• Executive power was vested in the British monarch, and the US President
• Legislative power was vested in the British parliament, and the US Congress. Once passed by the legislature, laws had to be signed by the executive
• Executive officers (e.g. ministers / secretaries) were nominated by the head of the executive

Given these similarities, we might ask why a "Parliamentary" system did not become established in the US. Why didn't the President end up adopting a mainly ceremonial role, with most of the day-to-day running of government being done by lower officials who would rely on Congressional support to enact their agenda?

The answer lies in some of the differences between the US and British constitutional schemes:

• The executive had the power to dissolve the legislature in Britain, but it did not have this power in the US
• Executive officers were required to serve concurrently as members of the British legislature, but were, in the so-called ineligibility clause, explicitly forbidden from serving in the legislature by the US constitution.

Both these changes militate against the adoption of a "Parliamentary" style of government in the US. If the government derives its power solely from Congressional support, then there must be a way (such as dissolution) to resolve a situation where Congress and the government are irretrievably deadlocked. And members of the government who sit concurrently in the legislature create a so-called payroll vote -- a bloc of legislators who can be relied on to support the government where necessary.

So we might ask why the framers of the Constitution made these decisions. They saw the power of dissolution as giving too much power to the executive vis-à-vis the legislature. As was stated in the Declaration of Independence:

He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.

If we look at the debates on the Ineligility Clause, we see the following exchange:

We have no way of judging of mankind but by experience. Look at the history of the government of Great Britain, where there is a very flimsy exclusion--Does it not ruin their government? A man takes a seat in parliament to get an office for himself or friends, or both; and this is the great source from which flows its great venality and corruption.

In other words, the framers saw the ability of legislators to serve concurrently in the executive as a potential source of corruption.