Some of them you can. Tax-exempt orgs that take tax-deductible donations will usually give you a donation receipt. It wouldn't be unreasonable to require that they also fire off a copy (well, in a standardized form) to the IRS as well. Mortgage lenders already send a standardized form 1098 for the mortgage interest deduction.

Things like out-of-pocket medical expenses and business expenses would have to be done manually. But that's fine! Automating 80% of the work is still better than automating none of it. And it would be 100% for the people who don't itemize (which, as I understand it, is the vast majority).

The number of people that itemize has dropped significantly after the 2017 tax changes. A quick search shows that it used to be around 30% of filers itemized, now it's 11%.

It would be easy for the government to send you its automatic, non-itemized calculations and give you the option of itemizing.