Offer: You would be extremely handsome (or beautiful, depending on gender) - easily the handsomest/most beautiful person in any large crowd…but you could never see yourself or find out what you yourself looked like (no photos or looking at self in mirror.) Also, your appearance would be very different from your current appearance, so memory wouldn’t help at all.
Sure, I avoid mirrors and photographs as much as possible anyway.
But I am already quite handsome – easily the most handsome man in the room at this moment. Of course, I am in the children’s department of the library…
I think it is entirely possible for certain people to delude themselves into thinking just that, or are you talking about a magic genie scenario?
If I could improve on my own looks…then yes, absolutely.
But to look completely different? My friends and family wouldn’t recognize me? Nonsense. Why go through that kind of hell?
But if you could turn a “3” into, say, a “6” (I feel no desire whatever to be a “10”) then, sure, I would happily forgo ever seeing my own image again. I can learn to shave without a mirror.
I’ve met a lot of people, young ladies in particular, who seem to have taken this deal.
I see lots of people daily who thought they took this deal but got gyped. I see them strutting around and think to myself, “wow, another one who doesn’t own a mirror” 
How would you shave or put on make-up properly? Put a Band-Aid on your forehead? Yank that white nose hair out?
Seems impractical.
I’ve never put much emphasis on my looks (as opposed to how I present myself to the world.) And frankly, I have had enough problems with people taking me seriously without having to deal with “She’s amazingly gorgeous - she’s probably stupid.” I’ll stay the way I am, thanks.
No. What do I care what I look like? I don’t have to look at me, except when I brush my teeth.
So basically you are offering all the perks of being goodlooking, without any of effort in front of the mirror, or the worrying about the microflaws you see reflected.
Of course I’ll take the offer.
oh… just to clarify, I’ll only have no reflection, there is no bloodthirst or being obliterated by sunlight involved I hope.
My wife likes the way I look, so there’s no reason to change. I’m decent looking enough anyway, considering I’m approaching the half century mark.
While not extremely handsome, I am still handsome enough where looks are a non-issue. In your trade-off scenario, I would be giving up something of marginal value without gaining anything of appreciable value.
I’m the most handsome man in the room already. I’m also the smartest, the funniest, the fittest, the richest, and the best-dressed man in this room.
Yeah, I’m the only man in this room too. 
Sure, why not?
I’m pretty good looking now, and I was kind of a knock out when I was younger, if I do say so…so no. I don’t see a benefit to the deal.
You’d pretty much have to be blind, right? How could you otherwise ever ensure that you don’t see yourself reflected in a spoon or some such?
I’d rather be ugly than blind.
I’m OK with how I look, and it’d be pretty weird to suddenly look totally different… but that doesn’t seem to be the point of the game. If the question is, “Is being extremely good looking worth it if you can never see yourself?” then sure… most of the benefits of good looks come from how other people treat you, not from standing around admiring yourself in a mirror all day.
Since I can never see myself that means I’ll never see that mole that’s getting bigger and changing color, which means I won’t have it checked, which will give it time to mestatisize, which means I’ll be dead from multiple cancers in five years.
All that just so people will say, “Damn, that’s a good looking corpse!”