Any good UX designer can come up with a solution for this in a couple of hours or less. There's just no motivation to make it happen because this obfuscation of data is particularly optimized and useful for the sellers.
You can approximate UPS/FedEX costs by fitting a trend line, they are decently modeled by a linear (base charge + K*distance) function, but when you go to buy the label you might be way off. This puts you in the lose-lose-lose of either eating the difference of wrong estimates, overcharging for shipping and losing conversions, or just making people hate you by increasing the shipping over the estimate. Making a shipping API call is noticeably slow, so most people require an interaction after the address is entered.
Tim Sweeney's hot take was that "the two hardest problems in computer science are cache invalidation and shopping carts!"
If they're doing that anyways, they should have everything they need to hazard a pretty good guess (and then they have an actual inducement for me to provide it).