I am probably way off-base here, but wanted to define a bit more about my thinking on the topic as well as get your logic.
I've been noticing this idea (don't go broke in limped pots) a lot more often lately.
Of course, it makes a lot of sense, but I can honestly say I don't remember hearing it, as a rule of thumb, until fairly recently. Probably was just expressed and understood in a different way, at least to my thinking.
It may be one of those things that I heard and was just intuitive, so I didn't acknowledge. However, I've been giving it a little more thought. Honestly, I haven't gone broke in a limped pot in quite awhile, mainly because I'm a nit and go broke w/overpairs too often to even afford limping, but it has struck me as an interesting rule of thumb.
To differentiate a limped pot from a limped pot you might go broke in, I guess it's necessary to define the pot as 3+ players. There are those odd occurrences where you may go broke in, like, a blind v. blind situation w/non-nut (but premium) hands like each hit a straight/flush/trips.
I think the limped pot most players get themselves tied up in reads like "Utg limps, 4 callers, I call in LP/Blinds and flop is MeMeThem," where "them" and half of "me" is better for the vil.
I see the reasons to not put a lot of money in limped pots after the flop in three ways: control pre, control post, and managing variance:
*No one controls the action, Pre Flop. Everyone's just speculating, and so are you. Hitting the flop hard can not surprise anyone, except someone who hit it harder and checked.
**E.g. Joe the limper limps UTG with A6o. You overlimp OTB w/A2s, figuring you have odds after all the limpers between you and UTG. You see 2-3-4-5 flop. Joe checks, guess what happens when Sarah, the mid position limper w/88 (or 44, or whatever) bets?
*No one controls the action, Post Flop. Position is vital. Consider your button entitlement to charge other players "limping" money. This way, you charge Sarah to see Joe's cards, but your flop.
**E.g. Getting C/Rsed after betting on the flop sucks. Getting C/Rsed and squeezed (i.e. from the previous example Sarah C/Rses your continuation bet, and Joe is left to act after your action) sucks worse. In the above, you're cooked anyway, but decisions are (or should be) easier HU.
*If you're playing to "get lucky," you're playing the wrong game. In poker (especially in LL casino poker) everyone's hoping to get lucky, but more are relying on it. Poker players can't hope to get lucky, for long.
**There are only 1 or 2 situations where you'd limp AA after many limpers, right? I.e. someone to act after your limp has announced a blind raise or someone with an obvious, obvious tell has indicated a raise. You don't want to go to the flop (in most cases) w/AA with 5 or 6 players, do you? If you do, you're nuts; if you don't, you have to realize that even AA has fairly little equity w/5+ players, why would you think AQ is any more likely to pan out for you?
*"I saw a cheap flop" or variations thereof are the beginning to most BB/strategy discussions. The poster is often thinking "I mean, wtf, I flopped trips, and dude's betting into me on the turn?" when the winner's holdings were a total F-in mystery because it was a limped pot.
** Seriously, and maybe this is a sub-point of above, if you raised PF with the hand you flopped trips with, bet on the flop and got shoved on, would it give you pause to consider? Extra information, in the form of more draws on the board, can make your decision decidedly more costly by deceiving you into believing your opponent's (or opponents') hands are weaker than indicated.
***i.e if you limp 37s from the button "for a cheap flop," flop is 339(rainbow), are 9's going to flat your bet or raise? Contrast this to the reaction you might expect if you'd raised the same hand PF, and how the action might proceed. Sure, you're probably getting it AI at some point, but past hand information can be equity.
Again, just some guesses as to the origins of this idea, but I'd certainly love to hear more reasons behind this, in case I'm missing something. Of course, this was all assuming relatively static, 100bb stacks.