Represenatives Elect President

What if instead of an electoral college, the US house of representatives elected a president every 6 years? Let's assume that we have a constitutional convention to not impeach just because getting rid of the president would be politically expedient.
 
Washington would still become the first president, and he would probably retire in 1794. He would likely be succeeded by Jefferson and Adams, depending on which party controlled the House (IOTL, the Democratic-Republicans had a majority from 1793-1797).

The most obvious consequence of this is that it would raise the prominence of the House of Representatives over the Senate and make the executive more dependent on the legislature. Gerrymandering would become an even more common tactic, to the point that there might be a constitutional amendment against it by the 1900s.
 
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