Short info
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Instead of disabling the mini game, or resorting to "fun" alternatives such as brute-forcing the locks with random chance or smashing them with axes, my approach ignores the problem at early levels and I discard the whole lock picking perk tree as broken and uninteresting for any play-through after the first one.

This is not to be taken as criticism to mods taking a more adventure-like approach to solving the problem. I just prefer to feel like a master thief who can open any lock at level 1 with only 4-5 picks and some patience. I prefer opening locks with Alteration after the spells become affordable, anyhow.

Rationale
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The lock-picking in Vanilla is too easy. For a non-combat based character, this means they will get really tough enemies at early levels, since they have no armor or fighting skills (not even destruction). To make this problem less harsh, I simply decreased the skill-gain from breaking picks and opening locks.

Recommended mods
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immersiveUI_LockpickPlus: http://skyrim.nexusmods.com/mods/1639
Less Lockpicks: http://skyrim.nexusmods.com/mods/11540
Lockpick weight: http://skyrim.nexusmods.com/mods/8263

FYI (uesp.net)
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The skill XP needed for the next skill level grows near-quadratically, as given by:
> Skill Improve Mult * skill level^(1.95) + Skill Improve Offset

Using a skill gives XP according to:
> Skill Use Mult * base XP + Skill Use Offset (?)

Lock picking XP sources
--------------------------------
0.25 base XP for a broken pick.
2, 3, 5, 8, or 13 base XP for successfully picking a lock.

Modifications to 'Actor Value: Lockpick' (skill)
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skill use mult: 45 -> 10
skill use offset: 10 -> 2
skill improve mult: 0.25 -> 0.15
skill improve offset: 300 -> 900

Changing offset to 900 means that to advance lockpicking from 15 to 16 you will
have to gain as much xp as you would in vanilla to advance lockpicking from 54
to 55.

Decreasing the improve multiplier to 0.15 means that the xp requirement for
skill advancement will not grow as fast, but still reach about the same value
as vanilla on level 100.

Reducing use mult and use offset grants very small xp gains on breaking picks
and requires the player to pick about five times as many locks to gain the same
amount xp as they would in vanilla.

With these values, the average xp gain value between picking an expert and a
master lock (82 expert, 132 master) is aproximatelly equal to the xp gain from
picking a novice lock in vanilla (100 novice).

Possible problems
------------------------
There may not be enough locks in the game to get 100 in lockpicking and the author does not care.