I've been running my own mail servers for quite a while and I can assure that this is total nonsense. No large email host charges a fee for mail delivery. There are some rogue antispam solutions that do so, but they are rare and only used by shady small email providers. There's even an RFC stating that charging for blacklist removal is forbidden.

You will sometimes have delivery problems, although the problem is much smaller than often painted. But they can usually be avoided if you don't send spam (many people send spam but like to call it differently - your newsletter you subscribe people that haven't asked for it is spam) and if you properly react to error messages and abuse reports.