Do you have a photo of you using the strap please?I just got a classic speedy 25 and bought a separate strap to attach to the handles when shoulder/crossbody carrying is necessary. I know people say not to do this now, but LV actually advised clients to do this for decades before speedy B was released in 2011. For smaller sizes (25 & 30) if you're just carrying normal stuff as opposed to bricks I don't think it will hurt the bag. And the new playing cards speedies (I think they're part of the new cruise collection that will be released soon) have straps that attach to the handles!
Speedy b looks like a gym bag to me, and the leather strips down the sides can get weird and wrinkly...
So, I vote classic speedy, and add a strap when you need it.