Tracking contractor payments in FreshBooks works fine for the accounting side: categorize payments as they happen, and the totals are sitting in your expense data whenever you need them. The gap is purpose-built 1099 tooling. FreshBooks doesn't flag which vendors crossed the $600 reporting threshold, doesn't collect W-9 information, and doesn't generate or e-file the actual forms.
Most businesses handle this by exporting a year's contractor payments and feeding them into a separate service built for 1099 filing, or by having a bookkeeper tally it manually at year end. Either way, it's a once-a-year scramble built on data that was sitting there the whole time.