I don't have the links, but I remember when Matt Smith was chosen for the 11th Doctor, they said there was a serious discussion behind the scenes about whether or not they wanted to have the entire show depending on such a young actor. (That seems kind of ironic considering the age of the companions and the actresses who play them.) But the producers said the were so blown away by Matt Smith's acting range and abilities, that they were sure they wanted him.
As for it hinting that the Doctor might not have long left, there's been a limit on Timelords regenerating more than 12 times in the past, but that is able to be circumvented (and the Master is granted another 12-regeneration cycle).
In The Sarah Jane Adventures the Doctor says there is no limit on how many times he can regenerate, so if there were an ending approaching, there would have been no need to make it clear to long time fans that the limit of 12 regenerations no longer applies.
Added after comment:
There's never been (as best I can remember, and I've searched) a reference to regenerations getting younger in-universe, although that has been seen before. (Lady Romana's 2nd body was younger than her first.) Also, their first body has to start young (as a child) and grow older, since we've seen, in the new series, flashbacks to the Master as a young child when he first sees the vortex. And if you look at The Master and his different regenerations, while his latest is very young, compared to previously, there's no obvious pattern of him getting younger.
I suspect it has a lot more to do with appeal to viewers and that TV trends tend to show us higher ratings are often tied in with younger main characters.