Thank you for sharing your opinions.
She won't be spending her time in the Master Sword just analysing numbers, she has feelings and will no doubt miss Link as much as he is implied to miss her. At the same time though it's quite sad to think that she has to leave just as she is getting to grips with what it means to be human.
This stood out the most to me, (going through my second play through) I am now starting to realise though that Fi does try to connect with Link and channel 'human empathy', such as on Eldin Volcano when the Mogmas state that a Golden haired girl was dragged through here before and the Fi ask's Link who do you think it may be? (If you answer The black robed Woman Fi says that Link's assessment is 10% rounded up. And if you answer Zelda she states something like a 97% probability), I really see how the producers of the game make attempts (not saying they didn't want Link and Fi to share a bond because it is obvious they do) to show how they connect, Fi really tries (to me anyway) to understand the Human Condition in the game.
I really like her character her Character development over Midna to be honest, it was cool and all how she grew to understand the World of Light and came to like Link and Zelda however to me Fi's development of a lifeless 'Robot' that does analyse data grows over time and is more stronger (or how I perceive it anyway) as there are not many scenes that do show how she begins to understand (mainly the one at the end where she compliments Link on their time together) however this left me at the same time; wanting Fi to grow more between Link (an perhaps the people around her) and disappointed due to the fact that they only added few scenes in of this. However I did notice that when Link begins finding the flames and when he completes his spiritual challenges in the Silent Realm, Fi does always wish him 'Good luck' and to me this really conveys her development between Link as at the start it was just 'probability and analysing'. When Link obtains a new Sacred Flame and she powers the Goddess Sword up Link does smile at Fi however much to my disappointment Fi fails to connect with Link, these scenes do strongly convey her character development with Link though as there is that magnetism between Link and Fi as Link grows to really like Fi as a friend and companion.
Of course however nothing beats the final scene where Fi states she has fulfilled her duty in aiding Link in his quest as the 'Hero of Legend' all be it the strongest scene really conveys Fi's emotional capability of the Human Condition as she does recognise the feelings she has as 'something close to happiness' which I personally thought was amazing how Nintendo did pull this off, as The Blue Repitle stated earlier on (and I did quote):
She won't be spending her time in the Master Sword... she has feelings and will no doubt miss Link... At the same time though it's quite sad to think that she has to leave just as she is getting to grips with what it means to be human.
I do strongly agree with what you say and it is quite sad (yes I did cry a bit) :p however the connotation from the start was that Fi's only purpose was to aid Link in his quest to become the 'Hero of Legend', however the character development (the few scenes) that are added do truly emphasise the disconsolate scene at the end where she does in one sense depart from Link however it does truly reflect the time Link and Fi spent together.
Fi was a great character to be honest and it was sad to see her depart but I am glad she does say that:
'It is the most precious Data on record.'