In my songbird exame there is no consequence for failure, thus you are 100% correct it COULD be resolved without die rolls. If, as a GM, I forced the party to roll initiative and step through the order until it was the rogues turn, which them let them roll and kill the songbird....I would have just ran a pointless combat, would you agree?
I could very easily see this becoming a roll-initiative situation! Consider the following - and I've seen similar sequences played for real at my table many a time, though never in my memory specifically involving a songbird:
DM: "There's a songbird about 30 feet from you; it chirps merrily a few times, then flies away."
Rogue One: IC
pulls out bow and arrow, takes aim OOC "I need some target practice and Grog always needs a snack - I'll shoot it down."
Druiddon: IC
notices what Rogue One is doing "No way are you shooting that bird!" OOC: "I try to stop him from shooting by grabbing his bow."
Grog: IC "Grog like birdie. With salt, and ale." OOC: "I block the Druid's attempt to interrupt the shot."
Magelet: IC "Sigh - here we go again. I'll keep watch on the countryside while you guys argue about a bird."
steps to a high rock nearby
DM: "Looks like I need initiatives for everyone except Magelet, and I'll roll one for the poor little bird - hey, maybe it can get away fast enough that all this becomes moot."
At which point we now have a combat involving 3 PCs and a fleeing songbird. That the PCs are opposing each other rather than the bird is irrelevant; it's still a combat, and whether there's any significant or lasting consequences won't and can't be known until it's been played through.