Earlier quoted context omitted.
"Unlike stocks which seem to be entirely traded on exchanges" - no. You could have bought stock directly from the company, in an IPO or secondary offering (where it does not go through an exchange), from an individual or broker not intermediated by an exchange, etc. You can keep stock certificates in a safe deposit box, and then later transfer them into your brokerage account, they have no idea what you paid for them…
Thanks for the clarification. To whit, the few retail equity US and Canadian trading platforms I've used (Schwab's, Interactive Brokers, Scottrade before they became TD Ameritrade, Questrade) also do not provide an explicit feature that purports to calculate capital gains, so Coinbase seems to be exhibiting feature parity with equity retail exchanges. Coinbase and other retail equity trading platforms do provide an e…
I cannot account for the discrepancy, but I use Charles Schwab, and it absolutely DOES calculate and display capital gains. In cases where I have moved a security into the account (rather than purchasing it directly within the account) I have had to provide original cost basis information for them in order for the calculations to be correct.