It's not about receiving. Receiving is the easy part. It is about the delivery of your own mail.

> you stop giving money to your mail host and get a different one.

I was entertaining the "host your own mail server" thought, I agree that if you don't host it yourself then you can change your provider if it fails you.

> if you don't host it yourself then you can change your provider if it fails you.

Even if you host it yourself :-). The key is to own your domain.

If I recall the domain is not the only issue, IP is also deeply involved or am I wrong?

IP address is involved in some receiver's reputation calculation. It's never involved when sending to a domain.

Sure but then your mail gets dropped on the other end: The main issue I had the last time I tried running my own setup for mails was basically getting an email to an outlook or live.microsoft address. My mails were dropped for no reason, effectively not landing in my friends mailboxes and without any error on my side to know that my mail was getting rejected.

This is when I decided to stop trying getting through with this and came back to paying a provider.

Who needs the transmission more - the sender, or the recipient?

Much of the time, when it's for signup verification, especially for a free service, they just write "don't use @live.microsoft.com" underneath the email address box. The user wants to be signed up for the service more than the service provider wants a new user, at least by enough to use an alternate email address. Enough cases like this, and the user quits @live.microsoft.com.