David Barr published an opinion in RFC 1912 (Informational) recommending it as best practice for DNS administrators, but there are no formal requirements for it codified within the DNS standard itself.
While weak, this authentication is strong enough that it can be used for whitelisting purposes because spammers and phishers cannot usually by-pass this verification when they use zombie computers for email spoofing.
Other methods for establishing a relation between an IP address and a domain in email are the Sender Policy Framework (SPF) and the MX record.
ISPs that will not or cannot configure reverse DNS will generate problems for hosts on their networks, by virtue of being unable to support applications or protocols that require reverse DNS agree with the corresponding A (or AAAA) record.
ISPs that cannot or will not provide reverse DNS ultimately will be limiting the ability of their client base to use Internet services they provide effectively and securely.