The problem is not necessarily the expense - there are a whole bunch of steps that need to be taken in order to ensure that the big hosts don't flag your mails as spam - https://support.google.com/mail/answer/81126.

And even if it seems to be working fine at the moment, there are no practical guarantees that this will not be subject to change: https://plus.google.com/+LinusTorvalds/posts/DiG9qANf5PA. Even someone as high profile as Linus Torvalds had to resort to the classic method of public shaming in order to get a prompt response.

Lastly, there is not much incentive even if I cared about privacy - my typical recipient is anyway a Gmail account, so Google can definitely construct a shadow profile for the sender even if the sender does not use Gmail.

Again, it is a classic problem of a heavily centralized internet.