It's been a few years, but in Shenzhen and Dongguan, most ATM's would give only 2000 or 3000. Every once and a while, 5000.
Then I discovered ChinaTrust (China CITIC Bank). 中信银行. A lot of their ATM's allowed me 10,000 per withdrawal when an ABOC or ICBC ATM next to it would limit me to 3000 or 5000.
I was using a HangSeng Hong Kong card to withdraw from my HKD account, so it was nice to pay only HDF15 per 10000 withdrawal.
Of all the CITIC ATM's I tried, I think I only ran in to one or two that only allowed 5000.
Now phone banking and WeChat/Alipay mean I need months and months to go through 1000 cash.