Currently I maintain weight-banded rate tables manually. They drift from actual carrier prices over time, leading to overcharging some customers and undercharging others. Native carrier API integrations that quote real-time rates at checkout (with optional handling markup) would let me stop maintaining tables.
Critical carriers for UK/EU: Royal Mail, DPD, Evri (formerly Hermes), DHL Express. US: USPS, UPS, FedEx. Should support rate caching to avoid sub-second checkout latency from carrier API delays.