All you people stating the Anima regeneration is currently fine are insane. The OP's suggestion is a good one. Currently Only people who play extremely casually would have anima continually.
If you ever have to teleport somewhere that is out of the region that you didnt plan on teleporting to ahead of time to favourite it, It Will Take you 24 Hours To regenerate
It is really easy to burn through alot of anima at once unexpectedly by doing class quests, Main Scenario Quests, Grand Company quests, etc. Think back to the pre-ifrit quest to kill multiples NMs that are all located wildly far apart. This would take Ages to do without teleporting and would cost an extremely steep amount of anima.
Then lets say a person who completes some of the previous activities mentioned continues to play on a regular basis. Which, lets face it, alot of us did not because a large portion of the community only plays for a small portion of time following each patch, giving those players PLENTY of anima while they wait for the next patch.
If they continue to keep playing and are level 50, they are likely to regularly do certain things:
-Moogle
-Ifrit
-CC
-AV
-Level Other Jobs
-Help Friends/Strangers
Because of the limited community in FFXIV, most player would have a difficult time deciding to just "Focus on Moogle" or something. They would likely try and join most shouts that interest them. However there are plenty more activities than there are favouritable points. In Addition to this most players are located in Uldah when LFG so Moogle and AV would cost a fair amount consistently. Inevitably players will end up teleporting to non favourited points sooner or later. And a player who played consistently and started trying to complete these tasks with a low anima pool would find themselves starved for anima, and groups dont want to wait for you to walk to Turning Leaf or Aurum Vale from Uldah!
A player in this situation would likely feel that he has to take a break from the game and feel that he would be better off playing something else for the 2+ weeks it will take for their anima to refill.
I think in a game where it is essentially acknowledged that the game world is far to large and empty for running around to be reasonable by giving us teleporting in the first place, that it's ridiculous to turn around and say the world is only unreasonably large enough to require teleporting if you are someone who plays this game inconsistently, otherwise if you enjoy the game and would like to play regularly you should also enjoy spending significant portions of time running around.
This is a totally ridiculous Idea. If I would like to continue playing then I dont need the game "telling" me to take a break! It shouldn't force you to take a break, you can always take a break if you want to. A player should be able to continuously play as often as they would like to.
Making people spend more time running around is not hard. It is just a waste of time. Time =/= Difficulty
So obviously you just leech teleports? Going "all over the world" with no more than 10 anima every day is pretty amazing! You teleport to one non region non favourited point, lets say unexpected Moogle (6 anima). And set hp to turning leaf. You win several times and are asked to teleport to grid one of these times(2 anima, 8 total).
Congratulations! You just spend 133% Of the Anima you gained in 24h to do one event.
And you're 4/5 of the way to your normal daily usage that you stated earlier in which you go "all over the world". Ok.