Yes, that can definitely be a problem.
I think you do need the pipe, or something else that works the same way.
If you just put feed in the bucket and leave the top open, the chickens eat from the top, throw out feed, poop in it, and cannot reach the feed when the bucket starts to get empty...
How big of a feeder are you looking for? Have you considered buying the kind sold for large flocks?
I'm thinking of the ones that look like this:
https://www.walmart.com/ip/Miller-Mfg-Hanging-Poultry-Feeder-Tubes/16629543
https://www.hogslat.com/40-lb-hanging-chicken-feeder-galvanized
The...