What $ percentage goes into the turntable, the arm, preamp, and cartridge?

It helps to have actually done this a few times. I can tell you that for sure a more expensive cart like my Koetsu is a lot better than the half the price Benz it replaced. But comparing the difference in cost with performance the improvement from phono stage and arm upgrades was far, far greater.    

In other words say you have $5k for arm and cart. $4k arm $1k cart will be way better than a more even split. Of course this is all based on your having done your homework in finding the very best value you can for each. If you spend $4k on the arm just because you dogmatically follow the rule and found one for $4k then all bets are off. But if you are doing your due diligence and finding the very best arm you can for around that spend level then yes that is the way to go. 

Also do not lightly dismiss little details like the hardwired phono leads. This one thing alone not only improves performance a great deal it also saves a tremendous amount of money - and time, and headaches - looking for a good interconnect. All these little things go together. 

One other thing, what you notice about cartridge prices is not only anecdotal, it is absent any experience with what those carts deliver for the money. It could just as easily be that there are more expensive carts because so many people have been misguided into thinking they matter so much that money is chasing carts instead of arms. Lotta superficial advice out there. DYODD.

Relax OP. The one above is easily shocked. It stems as usual from not having the slightest clue what he's talking about. Of course they don't mention the cost of the cabling. The phono lead in Origin Live arms is hard wired. Just one of their many strong points.    

You seem to have a bit of a wrong impression about the way they use percentages. It is nothing to do with going cheap and upgrading later. They are very much in line with your goal of having a balanced system.  

Read through everything on there, it is clear what they are saying. There is even the example of comparing a dirt cheap cartridge on a very expensive table/arm and how much better it sounds than the other way around. I have experienced this myself upgrading carts, arms and tables over the years. Any way you want to slice it you are miles ahead to get as good a table and arm as you can. Then don't go cheap on the cartridge, get something you think will sound real good. Just don't shoot yourself in the foot thinking you should spend as much on the cart as the arm. You shouldn't. Their formula is just a rough guide, but it is a pretty darn good rough guide.