That is what they promised, and why I signed up for Hotmail. It was free, it was great, it was _independent_.
It was 1995. I knew I would physically move within the global village, and I needed a permanent address. Microsoft very quickly bought this successful idea, crippled it but did not, to its credit and my surprise, completely kill it. My addresses are still valid, I still use them, and among the international spam, I can still receive messages from my friends.
Comcast offers a miserable storage space for a maximum fee and arbitrarily bounces emails when they do not come from the same zip code. Notifiying the recipient is obviously beyond their ability. That is true, they could do even worse and drop the messages altogether and never notify the sender either.
That being said. It did hurt me hard when Hotmail was acquired by the Evil Empire. MSN is as much as I can take today. If I have to see Microsoft in full letters, I'll puke my last ties with it and a long gone global, free internet. I'll just set some email server at home.
Without the OSS move, internet would have been a very sad story. I knew from the start that corporations would very quickly try to clog and profit from the communication pipes. Thanks to free OSes, nobody but old farts or young idiots has to use hot or g or rocket or whatever mail.
RIP Hotmail, and big thanks to the original creators.