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.