The problem with that is unless you get a religion relatively early, you will find that most of the cities on your continent have been converted and your missionaries will do basically nothing at that point. Unless you enhance them.
Its especially annoying when the AI gets lucky and gets faith goodyhuts or bumps into faith CS and can found a pantheon/religion much earlier than you can using just shrines. Pantheon on turn 7 from a civ that has no early faith generation options (not celts, not ethiopia, etc) before anyone can even research pottery for example.
I think this illustrates something not mentioned here: that there are several points in the game where you have to make a choice about what part religion will play in your victory.
1) "I didn't found a religion." Easy enough, just hoard your faith until late game and let the AIs fight over your cities. Pick up any faith buildings that come your way.
2) "I founded a religion late." Try to keep your faith in your core cities. Note who sends missionaries to your cities - the AI views this as hostile behavior, so regardless of that DoF, if a civ is trying to convert you, they are at least willing to fight. In this situation, where I founded late, and most of the continent follows another faith, I keep my religion in orbit until late game. If I need a late game prophet rush for tithe or happiness, it's still an option.
3) "I founded a religion early and the tenants I picked are just awesome." In this scenario, you push and push your religion out. However, you will sacrifice other aspects of the game. You can't build a temple and a bank at the same time, so what's it going to be? If I go hard for my religion, I first convert CS, then non-religious AI. You should let your own cities automatically convert and use the early missionaries to go for unconverted CS or AI cities. I typically do not try to convert another civ who has founded a religion unless they spam me and won't agree to quit. In this case, and it will happen every time, be prepared to go to war. (FYI: I have found adwcta's 'guide to playing small' invaluable in terms of early faith strategy. I do not copy the play style, but the tips on spreading your religion are spot-on.)
The point is, I feel that religion is up in the air until the medieval/renn era. When you get a sense of what the religious picture is, you can decide to continue trying to spread or hunker down and save your faith for later. Bottom line: don't be afraid to abstain from the early faith game if you don't feel like you can dominate. Let the AI bash it's head against itself until the time looks good much later in the game. People rarely report that religion was a critical factor in a victory. It can help, to be sure, but not worth sacrificing diplomatic relations in a battle you won't win.