I don't believe that's true, but assuming it is: so what? Chaos can lead to some very fun gaming. At the very least, it will be a learning experience for the new DM, and he'll be that much better for it.
It depends heavily on the DM. Its hard for most ppl to see they do something wrong and even harder to correct it. Going down the wild-houseruling road can prove fatal
Chaos is fun when it is in favor of the players...and usually it isn't/ or the players think it isn't.
I don't mind a bit of Chaos even if its against me, but I certainly feel safer when I know that the guidelines are followed.
Now this seems to contrived for me but I still want them to have the treasure and they enjoy the game as it is and I like to keep track of everything (that is what I am talking about that this may be an issue of style). Besides the take it or leave it method is there another method to use that seems less contrived?
Give them a reason to search there...like maybe their owners told them that each one of the PCs can choose one thing from the chest that is in the back room. Or maybe the whole chest is their reward. Or some other reason.
Usually, getting in someones house and grabbing stuff from a chest is named ''stealing''

So in this example, there needs to be a motive.
Hide the loot once. Then give them a gp reward for clearing the house later. Or add stuff to a later encounter.
Ohh and maybe I should say I never give random loot in fact I am found of letting the PC's tell ME what they see in the treasure hoard (they see a ring and a sword but they dont know how powerful those are so I can still regulate the treasure given); and letting them roll a d% to see what item comes up in the magic item compendium. And I give alot of gp which the PC's never seem to want to spend... maybe this is too lenient since they rarely get items they simply CANNOT use (like a Huge breatplate or something)... however they rarely use their items to their full potential (a long time ago I gave them a shield of blinding and the cleric who got it has NEVER use its blinding ability, for example. so I think it evens out...
How does this work? What level are your PCs? Some items are stronger than others- the cheapest magic ring is way too expensive. From a first glance at your system it looks dangerous, and I don't think it could work without book keeping from your part. Maybe changing this would save you lots of time that you could use preparing other things.
Im sure though that it is not the case that: either a DM must adhere to the take it or leave it method OR must adhere to the tally it up and reallocate method. There must be a middle ground. I was just wondering what other DM's have done. the take it or leave it method, while I may try it, I dont think is a thing that all experienced great DM's do (rather it is a thing of style since even some non-experiecne DMs will do that, i am sure many non-experiecned DM's use the take it or leave it method since bookkeeping is not that fun). Hoepfully this helps clarify my problem (if I can even call it that anymore, and yeah maybe "exciting" was a bad word to use I mainly mean more exciting for me to DM since the PC's will not be affected by my decision. ANd yeah once I write it out it seems like a weird question but I think the "either... or..." statement above gets at the heart of what I may be looking for...
Check how much total wealth the PCs have, compare it to DMG. If they are above where they should be, ''take it or leave it''. If they are below, ''reallocate''.
From personal experience, when your players will realize that there is loot around that they wont get if they wont search, they will metagame into ransacking the place even if they normally wouldn't. A Paladin that normally wouldn't loot a dead body will have to metagame himself into looting. But it saves you time.
So the real question is what you prefer. I propose turning what the players don't find into future quest rewards. This way your PCs won't notice that they will get their loot no matter what, and will not metagame into thinking ''whatever, he will give it to us later''. And you won't have to book-keep that hard.
Quest reward can be a house, gp, spellcasting support from a temple/strong caster for ''x'' spells, a very special service (like exceptional help from a sage for knowledge checks) etc etc.