The reason is plot. Period. If Kishi allowed Naruto to use his full speed all the time Naruto would be too powerful so he limits Naruto. That’s nothing new. Kishi has always held Naruto back. It just like how in part 1 Kishi didn't allow Naruto to summon giant toads with his chakra (he could do it with 9 tails chakra). Naruto could only summon small toads with his chakra which makes no since because Nartuo's problem with chakra control was he used too much chakra not too little. Just think about it. How can Naruto be able to mold enough chakra to create 100's of shadow clones, but not summon a giant toad. I'm not talking about a boss size toad either.
Naruto did train in speed. His battle with A was his training. In fact that was the entire purpose to that battle. Naruto was heading to the battlefield and A was standing in his way. Naruto was only allowed to use speed to get by A and he started out using the minimal speed he thought was necessary. That speed was not enough so he kept using more and more speed until he used his max speed (or close to it) to not only dodge A's attack, but also run by A as well.
Naruto running by A was the most important part of the battle. It's true that Naruto doesn't need to be faster than A to dodge A's attack, but he does have to be faster than A to run by him using nothing but speed and that's what he did. So, Yes, Naruto is faster than A.
