I know this isn't the answer you guys are hoping for, but Shopify will very likely not be adding dimensions to their platform in the near future. As the developer of checkout shipping apps, they are incredibly expensive to build and cost even more to operate, especially dimensional shipping algorithms. At Shopify's scale, their checkout couldn't handle it without increasing the cost of everyone's plan prices to increase server infrastructure, so they choose to have developers specialize in the area so only merchants who use the feature pay for it.
My parents are small makers and a common topic at family dinners is shipping costs (yes, I feel bad for other family at the table not in the indsutry lol) and how awful it is to lose money because they can't charge an accurate shipping price. Unfortunately, they also use Etsy which has limitations as well so they mimic their Etsy setup in their Shopify store. This leads to them sometimes spending hours handmaking an item only to realize it's shipping to the middle of nowhere and they end up losing money on the order. It sucks and I don't want this to be the reality of merchants.
Because of this, we made a standalone app of our dimensional shipping algorithm, SmartBoxing™. This is one of the most-loved features of Intuitive Shipping and I drove the build of it with our team to support merchants just like my parents. I also fought hard to make the entry point $9.99/mo for 100 orders, which we barely break even on (account management and server infrastructure is expensive).
If anyone is open to using a third-party app to stem the bleed of inaccurate shipping costs, I encourage you to try out Smart Boxing. We are free to install and configure and also offer a 14-day live trial in your store so you can take it for a true test drive to see the value it provides.