first you said a shooter and a turn based game are mostly the same but the time factor is deleted in turn based. i think most of turn based game give you time limitations just to prevent the game to be very slow.
True time has been added for the purpose of speeding up a turn based game, it's not the best reason to add time though.
I consider Final Fantasy XIII to be the worst at this and Dragon age to be best at it.
The thing about Final Fantasy XIII thy attempted to pull new players by removing turn based combat elements and instead thy only highlighted the worst of it.
Battles are in real time this means those few milliseconds that determine a battle is played back at full speed, so as no surprise battles are short ranging from 22 milliseconds to a whole minute for me.
This makes it very annoying that the game has combat in a separate space, the transition takes longer than most battles.
By having real time combat thy force players to spend more times in the menu, upgrading, stocking items and leveling up so that thy can prepare for those short burst of battles.
In truth this just changes the point of turns, now it's the players turn when thy first spot the enemy. Thy select there team change there gear and then when thy feel thy are ready thy play that little game where you have to run up behind the enemy and start combat.
The reason I personally like Final Fantasy is that thy provide a set of puzzles to solve, first there is combat but usually only bosses are really fun.
Second there is leveling, this is a long-term puzzle that each short term puzzle adds to, there is the story that is revealed as you play and finally there are the secretes that often take more than one play through to find.
Final Fantasy XIII falls short on all of these, because it's linear noting the player does really matters and this brings me to the point.
The thing turn based combat gives you more than any other game is control.
If you think about when turn based games feel the slowest, it's when your turn is over. This is not often a problem when fighting a NPC because the AI thinks fast.
Time is mostly added when it's PvP, just think how bad it would be if your opponent is losing and then decides not to make any moves till you quit.
It's control Dragon age gives you when you can pause the game. It gives even more control by making the enemies attacks weak, allowing you to clearly see large treats by monitoring your characters HP.
Don't judge turn based games by the hoards of bad ones, there are even more bad shooter clones.
One last thing, there is one thing turn based combat offers that NO OTHER game type does. Full control of more than one entity.
Even a RTS needs AI to govern the units you command, only in turn based games can you be more than one.