How are electronic records relevant? The information needed is expected, whether records or electronic or not, when doing capital gains now, so there's non rational need for electronic records.
> For other types of assets, the inflation rationale is still a decent reason to have a lower LTCG rate
No, it's not. For the reasons already explained.
The same way you prove cost basis; if you have adequate records of one, you’ll pretty invariably have both.
If lacking transfer documents makes the sale value “all gains”, then the inflation adjustment is irrelevant, since you are adjusting a zero basis value, which is still going to be zero if you do or don't adjust it for inflation, no matter what a amount of inflation has occurred.
The only place where there is even a theoretical problem is where there is proof of basis value but not basis date; this seems extremely improbable to occur in practice.
So you already need a receipt or some record with the original purchase price, which probably has a time stamp on it.
But yeah this is one reason why collectibles have a special, higher LTCG rate than securities.
No, it's a good reason to inflation adjust them; not inflation adjusting them and charging a lower rate means that people who can regularly turn over capital so that there is often very little inflation effect (more common with the really rich) pay low real taxes on income, while people who have a few capital assets that are held a long time for use value and then sell them with little real (but much inflationary) appreciation pay taxes at low rate on the nominal income, but often at a high rate on any real income (or, worse, pay positive taxes with no or negative real income). The two features compound the pro-wealth bias in capital gains policy rather than offsetting to approximate fairness with taxation of other income.
Taxes on income should be blind as to whether it is labor or capital income (including those characterized as “payroll” rather than “income” taxes), and, to smooth irregular income streams (which otherwise have undesirable consequences in a progressive tax system) generous allowances for deferment or unusually high income and advance recognition of income should be made, and basis values, and deferred and advance-recognized income amounts all should be inflation adjusted.