We could, and we could also build cars that run on peanut butter. We don't, because there is no point to it, because it costs too much, and because it solves problems that have already been solved.
It's not going to magically make inflation or interest rates go away. You are correct that the legal system would still be around, and will still be able to do pretty much everything that it's doing now.
It's not illegal, because it's not actually in the realm of the SEC. What you describe - the background implementation of finance isn't an investment, it's just boring clerical work. [1] If there were a better way to do it with blockchains, people would adopt it. Unfortunately, blockchains do not solve the hard problems in this space, but they do make the easy problems both hard and expensive.
[1] Yes, it's regulated, but the regulation allows for improvements. The regulation isn't the problem - getting everyone's workflows that are accustomed to how this clerical work is done is the problem! Nobody will switch to a system that's not better, and blockchains are not a better system for this [2].
[2] And if they were, no currently existing blockchain would be a better system for this. If stock clearing or whatever would somehow work better through a blockchain[3], there's no reason to do it on a blockchain that has already been pre-mined, and is being traded around by speculators. Why pay them a first-movers tax, when you can just fork and spin up your own? The hashing power of anything but BTC and maybe the ETH networks isn't sufficient to prevent attacks on something as important as this - so the existing coin ecosystems have zero value for this usecase. The organizations adopting this would have to control the hashing power, as well - and at that point, why pay third-parties for it?
[3] It wouldn't.