I have found that over time they learn. Initially my Commerce Bank (now TD Bank) branch wanted me to break the rolls and run them through the coin counter. I persuaded them that it really wasn''t necessary, they could just count rolls. So they started counting rolls. Then they went to counting trays: $125 per tray. This last time I went there they counted boxes and did not even open the boxes (they opened one box, peeked in, and trusted that the others were the same). They're learning, and for the better.
Next step: convince the Mint to drop ship the packages directly to my bank. I'm working on this.
And the final step in simplification: just call the Mint and tell them to deposit some miles to my FF account, no need to bother with shipping coins around