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If the market always "decides" gold is great, why don't cell phone contracts, insurance policies, mortgages, employment agreements, car leases, etc. specify payment in gold?

Because of legal tender laws and Gresham's law.

You can write a contract and specify payment in gold but if the other party doesn't pay and you sue them, you're required to accept payment in legal tender. You can't say "but I wanted gold!" Likewise, since you are forced to take legal tender if you want protection from the courts, according to Gresham's law, people would rather save their gold and pass off their paper currency to you. All of this serves to reduce the amount of gold in circulation as money and we get to the state of affairs like today where very few people could even pay in gold without first buying some with paper. That makes it hugely inconvenient and businesses don't want to shrink their market share. Remove the legal tender laws and have courts honor gold contracts and then you can make an argument. As it stands, when there is a truly free market, without government threats, the market prefers gold. You claim to be big on evidence so let's not ignore thousands of years of history.

You may have to take legal tender, but you can link the amount of tender to the exchange rate with gold. A gold clause still lets you do that and it's been perfectly legal to enforce since 1977. See 216 Jamica Ave. LLC v. S&R Playhouse Realty Co.. Gresham's Law makes sense but it also contradicts the idea that the market will always choose gold. You just named some important reasons that market participants will continue to contract in fixed quantities of fiat currencies instead of gold-linked quantities, such as convenience and retaining market share, even though it is legal to specify payments in terms of gold.

If market participants prefer gold, it's even more puzzling that gold doesn't dominate savings. Right now Apple is sitting on more than $75 billion in cash. Microsoft has more than $50 billion and Google more than $35 billion. They don't appear to be in a hurry to spend it. There are many large companies with multiple billions in cash on hand. Why not convert it to gold if gold is stable and fiat currencies are unpredictable? They don't need to worry about any market share loss or customer inconvenience from what they do with their savings.

Maybe 10% of those reserves are actually in cash. Maybe.

Then what are they kept in? I guess you aren't familiar with accounting, but cash means cash.

Not really. Mostly it means highly liquid investments, such as money markets. That said, the 'cash' position of any particular corporation; or even all of them taken together, is only part of the equation. You have to consider their debts as well. Although most large corporations are net positive, they aren't by much. They tend to own each others' debts via money markets, which are basicly mutual funds for corporate bonds. This is very similar to how the banks all seem to owe each other money. The idea that there is corporate cash sitting on the sidelines, or even private investor cash, waiting for the right moment to jump into the market is a sad myth. That money doesn't, for the most part, actually exist. And what doesn't exist can't be traded for gold.

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Regardless, you've sidestepped the question. If gold and silver are the ultimate mediums of stable value storage, when why aren't all these massive cash stores converted to gold and silver bullion?

As stated above, mostly because it doesn't really exist. And for that which does exist, much of it is invested in bullion, either directly or indirectly via the 'paper' metal funds. The thing about gold, is that it is as untraceable for corporate entities and very wealthy individuals as Bitcoin is for us. There are estimates about how much refined "above ground" gold exists in the world, but the thing about that is that no one can really ever know with any certainty how much actually exists. And if we can't know how much there is, we can't ever know who is trading the "shadow" supply on the margins. Also, there are other highly liquid investments that can do as well or better than gold; such as oil futures, or ag futures. With value levels at the top of the corporate food chain, it would be unprofessional for the CFO to invest all of the net 'cash' of the company in any single commodity, no matter how wise that particular investment might be.