Why don't we transact with securities rather than fiat money? I don't know a whole lot about economics besides for an intro course I took once so bear with me please...

I'm a software developer working with cryptocurrencies, and I got to thinking that it would be technically possible to tokenize securities (ideally giving legal ownership of that security to the token holder) and use them for transactions within an economy instead of currencies like the USD. One token would represent a certain percentage share in a holding company or a mutual fund or maybe even a government bond.

After looking into this, there seems to be some large legal barriers preventing this sort of thing from happening, and it would be more of a feat in that regard than on the technical side of things (I think), but, more theoretically, it got me thinking about what the effects of replacing fiat with securities might be.

One thing I've heard is that a mildly positive inflation rate is desirable in a stable economy because it increases the opportunity cost of holding money thus stimulating more spending. A deflationary means of exchange might reduce spending and cause bad things? I'm also aware that using fiat allows the Federal Reserve some control over the economy via monetary policy, which is definitely needed in this boom and bust situation we're in now.

On the other hand, securities actually have what all those gold-standard nutjobs want a currency to have, actual intrinsic value! It allows for anybody taking part in an economy to necessarily own part of it. It could be a kind of free-market socialism where the means of production is actually owned by the people (redistribution of wealth still needed of course). Furthermore, In today's world, the very rich tend to have proportionally more of their wealth tied up in investments compared to the working class, further widening the divide. If securities were currency, investing wouldn't be a choice but a requirement.

My main question is, why isn't this the way it works today? Certainly it would be possible for just a regular US dollar to be legally backed by equity or debt with no crypto hacking involved, so why haven't we done so?
You've just reinvented bearer bonds. From that page:


  Bearer bonds are bonds that are owned by whoever is holding them, rather than having registered owners like most other securities. Like most other bonds, they have a stated maturity date and interest rate, but coupons representing interest payments are generally physically attached to the security and must be submitted to the company for payment.


It's been done. Like cryptocurrencies, the one class of transactions they turned out to be well-suited for was the class of illegal transactions; money laundering, payment for criminal services, prohibited capital movements, etc.

And having a fiat currency which is simply backed by a country's economy, has succeeded against all other kinds of currency as the most viable.