Yes, I have a character who is a Chosen of Mystra.
Because I do have such a character, I can share with everyone some minor drawbacks to being such a Chosen:
Once you are Chosen, you are Chosen forever.
You may never stop being a Chosen of your own accord.
If you deliberately try, you will be punished.
If you try again, you will be punished more severely.
Each additional try will mean a costlier, more painful punishment until you stop trying (and you WILL stop trying, at some point.)
As a Chosen, your body does not age.
You will watch your wife grow old and die.
You will watch your children grow old and die.
You will watch your great-great-great grandchildren grow old and die.
You will watch your friends die.
You will watch as the world you knew ceases to exist, and you must endure in the new, strange, and alien world.
You will watch everything you held precious, everything you built, everything you loved, wither away, crumble into dust, pass into history.
You will be utterly alone.
You may be slain as a Chosen. This does not release you from being a Chosen.
You will become an undead Chosen.
As an undead, you will continue to serve under all the rules and restraints you had in life.
You cannot be destroyed by a cleric's rebuke.
It is probable that if you are killed again, after a time in the Outer Planes Mystra will send you back as a Celestial Chosen, to serve her on Toril.
A Chosen does as bidden
If Mystra asks you to slay your wife, you obey.
If Mystra asks you to slay your friends, you obey.
If Mystra asks you to torture someone, you obey.
If Mystra asks you to go on a dangerous (read: suicidal) mission, you obey.
If Mystra asks you to have children, you obey.
If Mystra asks you to use your magic to change your sex from male to female, and then to have children, you obey.
Disobedience means punishment, which will be swift, to the point, and severe.
Obedience is to be immediate. No argument. No hestation.
It is fine for you to think for yourself, and question (or even hate) Mystra's dictates ... but you obey them, regardless of what you think or want.
Being a Chosen is inherently dangerous
The Silver Fire was never meant to be held in mortal bodies.
The Silver Fire can cause permanent, irreparable (even by a Wish) insanity, brain damage, or damage to parts of the body.
The Silver Fire can cause you to wither quickly, turning into a Lich within a few years.
The Silver Fire can burn you to a husk, killing you in a most extremely painful fashion.
The Silver Fire, can simply outright kill you.
If the Silver Fire is harmful to you, there is no help for it.
Mystra will not help you.
The other Chosen cannot help you.
No other character (except maybe an Epic Sorcerer or Wizard) has any hope of helping you.
A Chosen is a slave
That's right. A slave. With a capital S. You have seen the branding of slaves in films, have you not? Think of the Silver Fire as one giant brand, covering all the body and filling all the body (and having the Silver Fire bequeathed to you hurts as much as such a theoretical branding would.)
You are the chattel of Mystra.
You had BETTER realize you are the chattel of Mystra.
Your entire existence functions to serve Mystra.
Your station is below that of all other mortals, for they have the Freedom of Mortality, and you do not - even though you are still mortal.
A Chosen is a target
Eager adventurers out to prove themselves want a crack at you, for you are one of the Legendary Chosen.
Every person out to make a name for themselves, is after you, for you are one of the Legendary Chosen.
Every enemy of Mystra, is out to kill you, for you are one of the Legendary Chosen.
Every servant of EVERY evil Power in the Faerunian Pantheon is out for your blood, actively or passively, for you are one of the Legendary Chosen.
A Chosen is trapped on Toril
That's right. You do not get to leave Realmspace. That is shirking your duties.
You get to leave Realmspace when Mystra ALLOWS you to leave Realmspace, and you stay gone for only as long as She dictates. Come back late, and punishment is your due.
Leave Realmspace with Mystra's permission, and refuse to return ... well, Mystra is patient, and has all the time in the world to find a way to retrieve you from where you are ... and when She does, may the gods help you.
A Chosen is humble
A proper Chosen is humble before Mystra, for Mystra is Magic Itself, and there is no Power more overawing and worshipful, than magic
A proper Chosen is humble before magic, appreciating that he or she does not understand it, can never truly understand it, and must function on limited knowledge - always a dangerous undertaking
A proper Chosen is humble, knowing he or she knows only a little of the whole of Reality with it's vast unexplored places
A proper Chosen is humble because being humble is a good survival tactic in dealings with others
A proper Chosen, is humble because humility is a virtue to be strived for
A Chosen is patient
A Chosen is patient, waiting and watching, measuring all that is seen and heard and felt for later use
A Chosen demands nothing, but may ask for most things - and accepts refusals with grace
A Chosen, knows that knowledge and power come slowly and through great effort and sacrifice - NEVER does power come instantly and cheaply
A Chosen is willing to wait years, decades, centuries, or millennia, for a given time in which to take an action
A Chosen does not throw around power
A Chosen does not reveal he is a Chosen, until it is revealed forcefully in a combat situation
A Chosen respects magic, and uses it prudently
A Chosen knows when not to use magic
A Chosen appreciates that he bears great responsibility, and lives up to that responsibility
A Chosen never acts impulsively, frivolously, irrationally, and never throws magic in anger, rage, or hate
A Chosen preserves the magic
A Chosen never destroys spellbooks
A Chosen never destroys any magical item
A Chosen never kills anything that lives, unless ordered to by Mystra, or to save their own life (and then, punishment may be forthcoming), or under special circumstances in which an understanding with Mystra has been achieved
A Chosen NEVER interferes with the spread of magic, no matter how it is being spread, or what the consequences of that spreading are - the Chosen always AIDS the being spreading magic
Is this what you want?
Better think it over ... there will be little enough time to think about it, if Mystra comes and offers you Chosenhood!