No, that sounds fun and flavourful. I'm picturing Vikings at the moment because it fits really well, but it would be a neat detail for all kinds of made-up cultures.
There will be published adventures that will go contrary to these expectations, and you'll either have to not use them or spend time adjusting them to fit into your setting better.
The big caveat is that there are player types that this would bring either no positive to the game or actually be a negative. Players who are there to mostly roll dice, have fun with their friends, and unwind without having to really think hard (a totally valid reason to play RPGs) won't work well with this, since that play style relies on using more standard RPG tropes and not thinking too hard about them or the setting's internal consistency. If you have a group like this, or even one player like this, running a game like that will introduce more or less significant friction that you'll have to deal with somehow. (Usually, friction means changing what you're doing, or changing who you're playing with. Sometimes the players adapt, but players are less likely to invest the energy to adapt and that's especially true of the roll-dice-and-unwind type of player.)
A lesser caveat is that you will have to think about how this interacts with the D&D spells that can bring people back to life. Is that an offense against the gods too? Or does properly burying the body permanently ensure the spirit's place in the afterlife and you can't bring them back (and those spells don't work)? If this bit of metaphysics interferes with the (somewhat) common trope of D&D being a game where dying is just an inconvenience, then that will require some adjustments too, either to adventures' difficulty or to your players' expectations, as above. On the plus side, if you and your group are sick of death being merely a speed bump (and enough people do dislike that side effect of D&D's standard spells), then that's a feature! It would be for me.
So long as you have a compatible group and you lay this out up-front – which you should do anyway if this is a major part of the players' characters' culture – this should be fine. Adding a reasonable explanation for where ghosts and ghouls come from is the kind of setting design that a lot of players appreciate. In this particular setup, the players may also come to appreciate that it means their enemies will be reluctant to kill them out of hand, too.
As for wealth considerations, in D&D Next you won't have trouble with wealth. Unlike its two predecessors, it doesn't make wealth required for them to meet an expected power level for their character level, because it has mostly done away with the concept of expected power level. (At least, not as part of the "core" D&D Next rules. Stuff similar to 3e's Wealth By Level or 4e's treasure parcels will probably show up in the modular optional rules.) Your suggestions for how to place "adequate" treasure seem eminently reasonable, where "adequate" in a system that doesn't super-care about wealth is defined by how much treasure you think should be coming the PCs' way in a given span of time.
I am having the same problem, although my characters just reached level 3.
However, I think that the best answer is for the party to better share the loot between each others. They, after all, are the ones who want to survive, not you.
If you have one player who always takes it all, he will create the imbalance, not you as the DM.
For what to "distribute", I use the tables on DMG p. 136-139. That gives me a way to determine the various types of objects I can give my players. The main problem is to avoid giving them way too powerful items.
However, I do not like to roll on the tables because I prefer to be in control to give the players exactly what they are likely to need (plus a little more).
Also, there are certain things that make sense. If you kill a mummy, it makes sense to find a Staff of the Python and if you kill a Wizard to find a Robe of Stars, for example. Plus, I prefer to offer items that make sense in the adventure rather than random things.
That being said, there is one rule that will limit a player from using all the items. If you look closely, there is a rule about attunement (DMG p. 136) which prevents a user from having more than 3 items that require attunement. So if you offer many of those, the one player who wants it all... would not be able to use the extras and may then start thinking he should share a bit more (because such items in his backpack won't do much good to the group as a whole.)
Another way to limit is to give similar items or items that the user(s) do not have proficiency in (i.e. give 3 short swords + 1, it is likely that people will stick to their existing weapon because they don't have proficiency in short swords. That being said, they'll need magical swords for killing those werewolves...) Also you cannot use two magical items of the same type simultaneously (DMG p. 141). So that's another way. Obviously, that could become quite a bit monotonous... but it could be a temporary solution to get everyone to have a similar power level. And the characters can sell or exchange the extras too.
Finally, there are items that require a specific class or set of classes (see Staff of the Adder, DMG p. 203). You could also impose limits such as race or size or even level... since you do not have to specifically use what the DMG presents. I myself use it as a large set of examples rather than the actual source of magic items in my worlds.
Best Answer
Loot/treasure should be the reward of another task, not a task itself.
You've already decided what the maximum amount of treasure you're comfortable with them getting. What is the point of "Well, I allocated 1000gp, but you only rolled 14 instead of 15, so you get 300gp instead"?
The players don't know what they missed out on, so why are you planning for it?
If you require "hidden" treasure, then I suggest things that are not checks.
When you describe the room (as a part of a greater habit of being more descriptive), describe inconsistencies. This allows the characters to solve the puzzle, rather than the dice.
Example: Exhausted after your fight, you take a moment to regain your breath. Blood from the slain orcs flows slowly to the south wall, glistening in the light of a nearby brazier.
This invokes the players to notice something odd "wait, what do you mean flowing south? Is there something there?".
No roll required for you to interact with them. They search the wall and you tell them that they find a door, revealing and old, banded chest holding 1000GP or whatever.
If you're dead-set on variable loot based on dice....
(which I disagree with)
Add multiple dice together for a bell-curve. 3d6 works well enough (I've used 3d20, but didn't like how much math I had to do). The loot you "want" them to have being between 8 and 13, then more or less lucky loot being closer to the outer bounds of 3 and 18.
One Caveat - Time
If there is a time constraint, then feel free to allow one (or all) of the players to make a roll or two. Then, the time doesn't allow them to keep trying.
Example: You slay the orcs in the room, but in the distance you hear an alert horn. You know that you need to get going, and soon. While a few seconds to look over the bodies probably won't kill you, taking any longer might. What do you do?