I am not familiar with PBEM, but from what you have written it's:

• Multi-player system
• Ability to play when you have time (no time restrictions)
• Ability to save the game and restore it whenever you like
• Combat is resolved automatically (no tactics)

Please enlighten me: why isn't it better than a saved multi-player game? You can set some reasonably long time for player to make his turn (of make the turns parallel), play whenever you both have time and then (when the game is quite long) save it.

I understand that having such option as ability to play whenever any of you have time is great, but no tactical fight...

The other person doesn't have to be online at the same time as you to play with PBEM. They don't even have to be awake. As soon as you say "play whenever you both have the time", you've missed the point. The people who want it care more about being able to play on a schedule that simply doesn't allow for simultaneous online multiplayer then they do about tactical combat.

It's actually a very old style of gameplay, people have done chess through snail mail for a very long time. In a lot of ways its a great system. You can play your turn while having your morning coffee, then go about your day. The other player six timezones away can do the same thing, or play on lunch break, or in the airport, or whatever happens to work for them. There is a ton of freedom in PBEM to play when you want against another human that standard synchronous online multiplayer will never match.

You missed the point by saying "both", meaning two players! The main reason actually is that you can have LOTS of people playing the same game without anybody having to wait every time two other playes are fighting (and one single fight believe me can be long in this kind of games especially in huge epic maps like those tha PBEM allows to play in all comfort). It is a system that works very well as long as everybody is serious enough to at least try playing one turn every day. I had the same perplexity the first time I realized that, by email, one loses Player Vs Player battles, but in the end if the auto fight is well programmed like in Age of Wonders, I personally experienced it as a great solution.

R2P could have such a feature too.   This is exactly what I want, hopefully better than PBEM.    But turns are at the same time, so technically it notifies all accounts at the same time that the turn is over, and they can do their next turn.

I've said before, and I'll say it again.   We should have some sort of decent quality automation (see "governor" thread)  so that you can have the option set the big strategy pieces in motion, and then  you might not really NEED to be there every turn.  Because for some part your kingdom manages itself.  You should be able to queue up actions and all that as well.

Whats more, it would be awesome if the notification was able to pull the weekly status report from the game.   So when you were notified, it literally had the recent events listed, as well as perhaps a review of enemy movement or other issues the player may need addressing.    So like if a monster appears on your land, or a plague hits one of your cities, you're notified so you don't let your kingdom go to waste because you thought the automation could cover the bland research, production, and economy choices of the day.