Lockpicking & Speech.
The lockpicking perk tree is basically only usefull if you happen to really svck at that minigame.
And when it comes to Speech; Well, if you sell and buy lots of things you'll automatically increase it a lot. As for the perk tree: if I couldn't use mods the perks that increase merchants goldsupply would be usefull, but since I can use mods that attempt to fix Skyrim's broken economy, they're useless.
Enchanting and Alchemy are essential if you want to have a good overall character
Really?
I'd dump Enchanting together with Smithing under the "Use only if you want to completely break the game" header. As for Alchemy: that one's a gimmick skill.
Neither skills are essential. You can easily get by without ever looking at them.