Wikipedia's article on Babson tasks says:
However, Yarosh's problem has a small flaw: the key is a capture, something which is generally frowned upon in problems.
(The "key" of a chess problem is the first move in the solution.)
Why is it frowned upon for the key move to be a capture?
I think that the feeling with regard to starting with a capture could expressed by saying that such a move is vulgar, This may or may not worry you
ADDED IN RESPONSE TO OP
Well, it depends on what you think is the pupose of a problem. For some, rather dedicated people, it is an art form, and the composition must follow strict rules, rather like a sonnet. There is strictly no point to asking WHY a sonnet has to follow those rules, but if you don't follow them it isn't a sonnet. And enough people think that the rules are good, that the sonnet form persists. And perhaps you can understand how a purist might regard a "sonnet" that did not obey the rules as vulgar.
But in the case of a chess problem there are reasons for the rules. When playing the game it is useful to look first at forcing moves, checks and captures. Problemists like to make the key move as subtle (and hard to find) as possible and so avoid the sort of moves that a player would be attracted by. Solvers find satisfaction is overcoming that difficulty. In the case of the Babson task, matching underpomotions in attack and defence is so phenomenally difficult to achieve that starting with a capture is regarded as forgivable.
Surprising key moves were a feature of the early problemist Sam Loyd. If you Google his name you may find some entertainment.
On the other hand, if you think of chess problems just as amusing puzzles rather than a minor art form, there is no real reason to accept the artistic conventions.
One reason is that a capture limits Black counterplay. So, if White had captures as options, the solver might well consider them first.
Another is more aesthetic, that a capture increases White's material advantage, and thus makes it less surprising that White managed to checkmate Black. It's considered a good thing if White manages to checkmate from a position where this might at first seem unlikely.
As an minor addition to the already accepted answer, it may be said that since the late 1860s or so 'it has always been that way'. The oldest 'rulebook' for chess problem composition that I know of is from 1878, and its second rule is:
- Capture of a man on the first move of white is not regarded as good unless intricate, beautiful, and numerous variations result from it.
(See http://www.anders.thulin.name/posts/the-art-of-problem-composition/ for the full text: the rules are at the end. It is quite dated.)
Earlier, in the 1850s, many 'good' problems were of the capture-early-and-often type, and were probably designed to show off a solver as someone who could find a forced mate in 18 moves or so. As taste changed towards more modern style (starting in the 1860s), this became old-fashioned and crude.
If you capture a piece as first move, that piece loses its significance. It could have been any piece, or at least one of several. Perhaps even a vacant square would have done. All other pieces are exactly the type they need to be for the puzzle to work.
This makes 1.XxY not exactly a cook, but akin.
