First of all, since you want to condescendingly tell people they should read something, maybe you ought to actually read what Reckless Attack entails. "You can throw aside all concern for defense to attack with fierce desperation," and later "recklessly." Note that nowhere in that description does that entail an "expense of precision," as you put it. An expense of personal safety, definitely. But precision: WRONG.
Swinging with Strength is not making a precise attack. Precision is governed by Dexterity. If you are using a Strength-based attack, then you are not attacking with precision, as Sneak Attack describes. That they tailored the description of Reckless Attack to try and describe the mechanics involved does not change the fact that Strength-based attacks are governed by force rather than precision.
And it's pretty easy to justify a burly Rogue (MC Barbarian) with a club putting aside concern for his personal safety in the middle of a melee to make sure he can zonk an enemy square in the head, which is very much a precision-based attack even if it requires STR to really make it hurt.
That is a rationalization. You have decided which end-goal you want to argue for, and contrived a scenario* which you think might justify it. It is not what the rules were originally intended to reflect, though, and the difference between intent and technicality are a prime example of how poorly-written this edition is.
Sneak Attack says you strike subtly and exploit a foe's distraction, and the mechanics reflect this by saying you must use a suitable weapon - a weapon which can be wielded with precision, rather than force. When you say that you can still wield that weapon by force, you demonstrate that you do not understand
why it is considered a suitable weapon in the first place. If you were going to allow Sneak Attack by force, in flagrant disregard for what a Sneak Attack is supposed to represent, then you should equally be arguing for Sneak Attack with a mace or morningstar.
* For the record, though I doubt it will convince anyone, your scenario isn't actually rules-legal. A club is a
light weapon, but it isn't a
finesse weapon, and Sneak Attack requires a
finesse or ranged weapon. The only finesse weapons on the basic weapon list are: dagger, dart, rapier, scimitar, shortsword, and whip.