std::span doesn't have at() because std::logic_error was a mistake. Using std::vector's at() is a mistake (you could use it as a helper method and make it as if it throwed std::runtime_error, but it doesn't, that wasn't its intended usage).
All three major C++ standard library implementations have an option to enable assertion checks in both std::vector and std::span operator[]. Enable them unless you are in such a resource limited environment that you can't afford the checks (unlikely). The only reason the standard doesn't require the checks is to allow C++ to be usable in those resource limited environments. You could argue the checks should be enabled by default, but that's not something for the standard to decide, complain to your standard library vendor.
It's not just the indexing you have to worry about, though. It's also out-of-bounds iterators. And while, yes, you can tell your implementation to emit checks for those as well, it's so slow in practice that nobody uses it in optimized release builds (and some implementations don't even support such use).
All three major C++ standard library implementations have an option to enable assertion checks in both std::vector and std::span operator[]. Enable them unless you are in such a resource limited environment that you can't afford the checks (unlikely). The only reason the standard doesn't require the checks is to allow C++ to be usable in those resource limited environments. You could argue the checks should be enabled by default, but that's not something for the standard to decide, complain to your standard library vendor.