When you pay cash by mail do they use your return address as part of the KYC?
that would generally be insufficient for KYC. i haven't seen people doing cash by mail in years anyway.
this is all dependent on where you live and do business, but in the USA the lowest MSB reporting threshold is $2000. that means at $2k or above, you should probably be collecting name, address, government ID, taxpayer ID, and date of birth. https://www.fincen.gov/money-services-business-msb-suspicious-activity-reporting
all of the cases i've seen where localbitcoins traders were arrested/charged involved high volume traders dealing in single transactions above $10k without AML/KYC. >$10k requires mandatory CTR reporting so it's an obvious threshold to be careful of. https://en.wikipedia.org/wiki/Currency_transaction_report