I didn't intend them to be in conflict - I listed a toy model, and acknowledged the limitations of it.

An explanation of ODEs and instability (some math background is obviously required): https://en.wikipedia.org/wiki/Stiff_equation

You lead with a fairly strong statement presented as a known fact and then later indicate it's just a model.

To me the idea of slowing things down sounds vaguely sensible, but I also know that I don't know enough to really judge. So it sounds like no one else really knows either, but the entrenched players like things the way they are, which makes sense, because the ones who have the money to be at the table running things are probably also the ones who have the money to throw at HFT and come out ahead.

It is a well known fact about dynamical systems in general.

I.e., if you ask me about the stock market, a flight control system, an electric circuit, a biological system and a computer network, I'll tell you that continuity gives you a better shot at stability than discretization in most of them.

I.e., if you don't know what you are talking about, lean towards continuity. If you do understand things, then explain the mechanics and back it up with empirics.

The hypothesis being advanced by people proposing point-in-time clearances is not necessarily that it will make the market smoother. It's that it will free up a lot of resources for other purposes.

For what it's worth - and not to distract from your real point - Exponential (or the more general Lyapunov) stability are a better explanation of instability. Stiffness is more a property of the method used to solve the ODE, rather than of the ODE itself.

Stiffness is a property of certain dynamical systems, which certain ODE solvers are better suited for. That said, "stability" is an ugly word in numerical methods, particularly for differential equations, as it could mean a number of things. I think this is the source of the confusion here.