Why is it that US Presidential candidates do not issue formal written manifestos of their intentions if elected - as British political parties are required by custom to do?
The United States parties do.
A political candidate is not a party. While the US president is the single most powerful figure in US politics, the president is not the only figure.
The president has more separate effect than any individual legislator.
The upshot of this is that a presidential candidate's views matter more than any other candidate's. So people listen to what the presidential candidates have to say over what their official platforms say. And it's understood that presidential candidates don't feel bound by the party platforms (even though they help write them). Which makes the party platform less important.
Donald Trump was notable though for the vagueness of his answers. There was continuous comment about this throughout the campaign. Outside his big issues, he avoided anything like details. And even in his big issues, details were a bit fuzzy. He wants a "big, beautiful wall" rather than a brick, concrete, or metal wall. He traded on his wealth as proof of his ability. This isn't a natural characteristic of the US system, most presidential candidates attempt to meet a higher standard of detail. It's unclear if this will become the new normal.
It's also worth thinking about one of the big differences between the US system and parliamentary systems like used in the United Kingdom. In parliamentary systems, people can't vote for a prime minister. And a prime minister doesn't necessarily last through the whole period. David Cameron resigned, and Margaret Thatcher was voted out. I don't have an example of a prime minister whose coalition collapsed and was replaced by a prime minister of a different party, but it can happen. As such, the party position is more important than the prime minister's.
In many parliamentary systems, the party also controls membership. So it is rare for politicians to abandon the prime minister on an individual basis. The party platform (or manifesto) is more important in that case because it is enforceable. In the US system, politicians are encouraged to break from party orthodoxy. It establishes that they view their voters as more important than their party ties.
There are still some mechanisms for controlling party members, but they are weaker. A politician who can't get a plum committee assignment or leadership position can switch to a different office. Representatives can become Senators or governors. A Senator can become a governor or president. A governor can become a Senator or president. As Donald Trump proved, party support is not necessary to win a nomination much less an election. And while executives need legislatures to accomplish things, they aren't reliant on them for their positions.