More likely you'd just have the same president for several decades, not several presidents in one month

I guess it depends how likely it is you think the few people that do actually change their votes from election to election and "how to change my vote" searchers, presuming that story is real would want that.

No restrictions on who people would vote for might be an interesting factor the US hasn't seen before. You wouldn't need political parties, or even to want to be president, to get elected. Maybe a president that appealed to lots of the electorate and kept doing popular enough things could stay for a long time?