There are a number of things that influenced the problem of electing the president at the constitutional convention:
1) the lack of established politicians and political parties in the US at the time - the person chosen would not have been a well-known politician whose views are predictible
2) they remembered the absolute rule of the English king, so they were worried the new president could also be a dictator - they wanted to make sure that the president was chosen in fair election and could be removed from the office if necessary