I think it will make the building progress much more faster as the builder do not need to get the resources from a far away storage
Try placing an input bin near the construction! Then you can assign some hearthlings to be only builders and some to only haul. It works!
It does work great indeed! Even before input bins I was using a similar trick, but now that we have them we can designate “priority materials” which will never run out during construction and that makes some sorts of projects much smoother.
For really large construction projects I sometimes use stockpiles to mark out the planned footprints* of the building/s, and let them fill with the required materials while I’m designing the buildings. This has the added effect of making it easy to design the templates in smaller sections so that the game doesn’t have difficulty processing the really large structures, instead seeing them as separate buildings (although I miss the old functionality where building a new template between two existing ones would connect all three; I also like some of the options the newer rendition opens up.)
*the stockpiles actually go in the spaces between the buildings so that the foundations are clear for building in ASAP; often I’ll put the stockpiles where roads will go later or I might put the roads first and then put stockpiles on top of them. I always keep a few input bins as well for “priority materials”, and if the project includes any workshops or warehouses I’ll build them first so that I can move the input bins and other storage containers inside ASAP and avoid the happiness penalties from messy roads.