Algebraic types, by themselves, don't do anything to make things "scary" or Turing-complete. Even C has (sort of) a weak, limited form of algebraic types through structs and unions. Zod, which you linked to as an example of the "simple, fixed, runtime types" you're advocating for supports discriminated unions too.

"Algebraic types, by themselves, don't do anything to make things "scary" or Turing-complete."

That's what "offer enough degrees-of-freedom to become scary" is getting at.

The types themselves are no more complicated than non-algebraic types in the end. However it so happens that for historical reasons they have appealed to certain personality types who proceed to build glorious castles on top of them, and indeed per the "degrees of freedom" point, multiple different overlapping-yet-often-conflicting castles. It is easy to mistake those castles as being "algebraic types", which is not helped by the name, rather than being simple things which can be explained to children and could easily be used in an introduction to programming curriculum rather than conventional types.

Conventional types are also not necessarily that complicated, or don't have to be. For instance, the complexity of C++'s towers of subclasses and templates should be accounted to C++ itself, rather than as a fundamental aspect of conventional type systems. There's things like Go that use a much simpler type system that is not generally amenable to such towers of complexity, which is a rephrasing of the most common complaints against it.

It's like a Go-kart that can do 100 mph - while not inherently dangerous as the excess capability is not necessarily advertised, and it requires and user to exploit them, and it's up to user consensus that how fast a go-kart should be allowed to go, as capability increases so does the potential for abuse. It's up to debate that how much is too much, and while I'd think most people would agree that 100mph is above that limit, some would still argue it's artificially limiting.

Powerful type systems are like that. You can program almost everything with what, for example, Go gave you before the generics update, but some would argue that more stuff is needed, like sum types etc.

Now as capability increases, and some comipler people boast that their type system is Turing complete, I think you are in fact vindicating people who decide to write things like a type that can only contain prime numbers.

But adding a type system this powerful will probably affect the real-world usability in your language, first you add a second language to your code that's awkward to use, slow to execute, and prone to crashing the compiler.

I remember having endless debates with C++ people arguing that their doubly-recursive template system, is not in fact, clever, but makes every compile take forever, is prone to crashing the compiler or making it misbehave, and cricitising it is not in fact, just an admission of one's intellectual inferiority.

Thanks, I didn't know that about Zod (https://zod.dev/api#intersections). But I suppose I could generalize my point to be "less is more when it comes to algebraic types". A little ketchup is good on fries, but no-one wants fries swimming in ketchup.