Questions about what shoes to use with what kind of lifting and training seem to come up as often as Kardashians show up in the public consciousness. Like the Kardashians, as far as I'm concerned, they pop up far, FAR too often. This has to be part of a larger marketing conspiracy that exploded way back in the 1980's when Nike teamed up with Michael Jordon and created the illusion that somehow shoes were the key to peak athletic performance. Strength training chicanery simply must have followed suit.
I mostly train with Chuck Taylors for two key reasons: they're cheap and they're what I have. With my limited funds and my near-constant traveling, I'm forced into strength training minimalism largely by necessity. That has drawbacks that I largely don't mind. Just like growing up poor teaches you more about living life than growing up privileged, training with nothing will teach force someone to make more out of less.
As we were all playing around with pulling a truck, many of the guys in the group struggled with driving with their legs because they were up too far on their toes. I explained to everyone that they need to think of their feet like their hands and get a good grip on the ground by making sure that with each step by planting as much of their foot on the ground (balls and toes of the foot) with each step.
I'm not completely slamming specialized shoes, or anything else for that matter in aiding weight training. Where I in a competition and I had the means to buy a special pair of shoe for every event to maximize my chances of winning, I'd certainly do it!
Your work-out gear doesn't make you strong. It didn't make Michael Jordon one of the most legendary athletes of all time and it won't make you fantastically strong. Your head and your body are responsible for that. If you don't have those two things in check then the only thing that your shoes buy you is credit card debt.
SO TRAIN AND STOP WORRYING ABOUT SHIT THAT DOESN'T MATTER.