If a Bitcoin could be divided a trillion trillion times, would this make a satoshi more useful and stop dust and future proof bitcoin for hundreds of years?
Yes/No?
I'm not sure creating the ability for more dust will somehow stop dust, but it would certain future proof bitcoin some more. Unfortunately, this probably will occur over & over as computers can only handle numbers so large at any given time and the need for bitcoin continues to increase.
Regardless, I don't believe handling dust is that big of a deal. It has been 4 years and the block chain is less than 15GB. I'm sure well find ways to compress it better, and even if we don't, you can purchase 2TB hard drives for $100.
Not to mention, transaction fees were specifically created to help miners cover costs to keep the network alive. When/if dust starts becoming a problem, transaction fees will increase for that dust making it prohibitively expensive - kinda like it does now except the block reward acts as a transaction fee subsidy so miners are allowing all kinds of dust for free/cheap because the amount they are receiving for maintaining the network is well above the electricity/storage necessary to process transactions.