I think smart contracts would make a lot of things in life easier for example you could do more things without a notary as most paper works could be stored digitally and uneditable in the smart contract and nobody could deny it as blockchain technology is not changeable... there are endless ways to use this new technology for a much simpler life but tho it would make some people unemployed and so they would need to do something else... still this was always the way to go, some people will benefit while others will lose.. thats life I guess.
Do you mean blockchain to store the documents? That is too costly. I do not think business will use something that is costly and do not provide them any tangible or intangible benefits just to show that they are tech-savvy.
I think it can be put somewhere in some practical application like distribution of hall ticket to student. Like Department A sent it report for a student that student attendance is ok. Department B sent report there is no pending dues for student and smart contract now send the digital Hall ticket.
So much manual coordination can be saved here that require reading report from multiple departments and deciding the next course of actions.