That kind of thinking is fine, but you have to look at the flip side as well: the balance so to speak. When you start your first Death Knight the first thing you want to do is go to Elwynn Forest and level your mining, right? Of course not! You will want to do the new DK only quests, see the new gear, get immersed into the storyline, and play with the new abilities to see what all they do! I know at least for me skilling professions up from the bare minimum is going to be the farthest thing from my mind, regardless of availability of mats and/or money to buy them up from the AH. I'm going to be leveling my DK, finding out spell rotations, stuff like that, and hopefully skilling professions as I go like any other brand new toon.
Higher level toons that either neglected their professions or are dropping a profession for a new one of course have to back track to get their professions higher, but those toons did not start at that higher level: it was a player choice that set those professions back. This is Blizzard's decision to start the DK at higher level, so it makes perfect sense to give a 1-time skill boost to professions.
Same with weapon skill: it should start out at a skill level = to the DK's starting level. I believe this for a couple reasons. First is from a lore and RP standpoint: the DK is a fallen combatant, risen up as a servant of the Lich King. Through death, does the person suddenly forget all their previous weapon training? Or are they still as proficient in the use of weaponry as they were before their death? I think the second.
The second point is from a more practical perspective: you realize how difficult it is to kill something at level 55 with a weapon you never bothered to skill up? Parry, miss, miss, dodge, block, 3 damage, miss, miss, parry. Yea, that doesn't seem like a smart move in the slightest to me. At the very least, the DK should start with a 2H sword skill = to its level, and the rest of the weapons can be unskilled, simulating a character who has only used one type of weapon throughout their leveling (2H sword because the DK starts with a 2H sword as their weapon, just in case anyone didn't get it).