The BEST flushing end production dog I've ever hunted pheasant with was a beagle. (I've pheasant hunted a lot of days/years with a lot of dogs) With the hound nose she didn't miss many. She was fantastic, especially in heavy cover or with runners. There were many times she would come out a mouthful of feathers (tail feathers mostly) this was of course after they finally took flight. She was low enough where she could get under the milo leaves before they turned the field. She was really good at keeping in range.
She however did not fetch the birds. Locate the downed bird yes, fetch nope unless it was a ball then all day. She also didn't bark (bay, howl, what ever you call the sound beagles can make) when pheasant hunting for some reason.
The downside to beagles is the desire to follow the their noses without any thought of....well...anything, so they aren't "running away" as much as they get lost after trotting around all day when they got loose. A lot have real bad problems with howling. This paticular one didn't. Several others we had had no interest in Pheasants.
So the are all Beagles good pheasant dogs? No way, but the few I've seen that would do it exceled at it paticularly this female and she lived to the ripe old age of 15 and was always ready willing and able until she got around 11.