It would be highly profitable for ShipStation if you where to implement this feature:
1. Collaborate with BigCommerce to enable bigcommerce to request real-time shipping rates from ShipStation (who would request it from the users configured carriers)
2. After ShipStation provides the realtime rates back to bigcommerce, have bigcommerce display these rates in the shopping cart "Estimate Shipping" and during the Checkout process.
This will really make ShipStation stand out as an attractive option for bigcommerce users looking for better shipping management.
The ShipStation API already provides support for retrieving shipping rates. It would not be too difficult for BigCommerce to add support to pull in real-time rates from the ShipStation app.
Perhaps it would even be in ShipStations business interests to write the integration yourselves on behalf of BigCommerce. That way bigcommerce users would have added incentive to sign up for ShipStation, since then they could get real-time shipping rates in their Checkout that match up perfectly with their shipping costs (prevent undercharging for shipping) and would even show real-time rates for carriers that ShipStation supports but that do not have native integration in bigcommerce.
Please vote for this feature request 😉