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.
I love being able to transact without the payment processors knowing anything about my customers, and they appreciate it, too. My cash payers are usually very grateful.
Some smaller banks in Australia do but the big ones all have cash and coin ATMs which are free for account holders.
Card only business can definitely evade tax too and many do.