Reportedly, Moffat wanted to go older, but Matt Smith impressed him enough to change his mind. That speaks volumes.
Nobody has shown better care and understanding of Doctor Who than Moffat, and that goes back to the short story he did for Decalog 3 in 1996.
Finally, some age comparisons -- this how old the various Doctors were the year they started playing the role:
William Hartnell: 55
Patrick Troughton: 46
Jon Pertwee: 51
Tom Baker: 40
Peter Davison: 30
Colin Baker: 40
Sylvester McCoy: 44
Paul McGann: 37
Christopher Eccleston: 41
David Tennant: 35
Matt Smith: 28
The point here? Tennant was already the youngest-but-one to snag the role, and any complaints about his age were silenced by the time "The Christmas Invasion" was finished. Let's let Smith play the role first, hm? (Yeah, sure, like that's gonna happen....)
Besides, the last time there was a hue and cry over who ever shall replace this incredibly popular Doctor who has won the hearts and minds of so many (Tom Baker) they went with the youngest Doctor they'd ever cast up to that point (Peter Davison, a distinction he held until, well, today). So it's tradition!
Finally, none of this is new. Every new Doctor has been met with tiresome complaints and confusion. The Internet just magnified it. Jon Pertwee was a comic actor, and people were concerned he'd be trying to out-clown Patrick Troughton; instead, he played it much more straight. Tom Baker's résumé was mostly villains, so folks were expecting a darker Doctor. Finally, the same people who thought that Tennant is an impossible act to follow were saying the same thing about Christopher Eccleston three years ago.