Unless you're handling huge amounts of cash, cards are WAY more expensive to deal with IME, especially because the fees scale as a percentage of revenue, so you can't just increase sales and lower your margins.
I bought a cheap cash and coin counter for about $400 on Amazon, which means it takes me about 2m to count whenever I need to balance the register.
For reference, with my POS I pay about $400 per MONTH in card fees (square).
It does take time to bring it to the bank, maybe 5-10m a week for me.
My bank does not charge for deposits or change; this would be insane and I've never encountered this in the US.
Counterfeits aren't generally an issue for small bills in practice; for $20+ we use a 50c testing pen that takes about 2s per transaction.
Sticky fingers are easily caught by balancing the register after each shift which is again about a 2m operation with cash and coin counters.
Overall I would be taking home about $500 more a month if all my customers paid cash, which is a big deal for a low margin business.