Losing quests? That sounds strange, but then I've always used Identify so I don't know.
I play a Warrior. I did take Identify as one of my primary skills (beefed it up as quickly as possible) for convenience. I didn't bother with Repair as I'd often be dropping off loot before any of my equipment broke. I never used Alchemy as there were enough potions available and you could purchase them readily. And I only took Lock Pick as a secondary skill to complete the Theives Guild quests. I have opened almost every door and chest in the game with the correct key or lever. There do seem to be a few chests, mostly as treasure rewards, that do not have keys though.
It comes down to personal preference. Enjoy!
