More of a question, are boots absolutely necessary?
I remember when Udyr didn't need boots but even now champs like Shyvana and Yi don't need them. It leaves a slot for a stat item and since they're high mobility to begin with is it smart to swap it out?
Well you would give up being fast for being... average? Sometimes a little below average.
Or you could buy boots and go REALLY fast.
well back in the days where adcs would buy boots early and mid game but at full build would flat out trade it for a zepyr/ buy 2 
like 
used to do.
But for real, boots are an essential thing... at least until 
rework storms the front and maybe changes 
around as well. Boots are very key to both being able to catch up and to get away from danger, while also making it so there is no inherent way to have an offensive boots that give you a crap ton of pure damage, it is always secondary damage/enhanced damage, pen/AS, or purely defensive/utility based. As some champs that live at running up to you to push buttons to be useful is so needed. 
, which cannot be achieved without the role boots fill in the game.
but in essence, udyr may not need boots, but if he can be fast enough to catch up to targets super fast, thanks to boots, (and the wave that was %MS items amongst the ADC update and 
) there is no reason to question it over damage, as if you can't catch your target you can't do damage at all.
