With district boundaries you at least have a candidate who has to live in the district and is (or can be) both familiar with the district and familiar to the district's voters.
Not necessarily. In NY they do not have to live in their districts. That's why SPM was shamed for wanting to run in the district he lived in and not in the district that has the same number as the former district he lived in (and represented). That's also why Mondaire Jones chose to run in the Manhattan NY-10 even though he lives in Westchester County.
District-based voting is a remnant of the world where political parties were not important and people did not really know the world outside their district. They cause more problems than they solve in the 21st century I think.
For one, how do you draw the boundaries? There is a danger of gerrymandering, of course, but even without it, population patterns itself can befuddle fair district drawing. Look at the fight in Alabama. One majority black district or two? And should not voters decide elections? With districts, elections are often decided at the time district maps are drawn up. At least for most districts/seats.