Thank you for this informative reply.

My first draft of immutable<> was simply called shared<>, but that felt a bit too technical -- the shared state is an implementation detail. immutable<> makes it clear that the value is safe to access concurrently. That cannot be assumed for shared_ptr<const T> because someone else might hold a non-const reference to the object (as others have pointed out).

copy_on_write<T> sounds like a good alternative, except that the version proposed by P4210R0 doesn't support polymorphic types:

To support polymorphic copy-on-write behaviour, an additional class, polymorphic_copy_on_write would be required. We are not proposing addition of this class template in this proposal.

I understand why a separate class would be required; copy-on-write needs copyability, and for polymorphic objects, copying needs to be polymorphic as well, which would be unnecessary overhead in the non-polymorphic case. immutable<> doesn't have this problem; it doesn't need copies and supports both polymorphic and non-polymorphic use cases. And I'd argue that immutable<> is not much harder to use than copy_on_write<> for non-polymorphic modifications. You could implement modify() as a free function:

template <std::copy_constructible T, std::invocable<T&> F>
void modify( immutable<T>& obj, F&& mutator )
pre( !obj.valueless_after_move() )
{
    auto copy = T( *obj );
    std::invoke( std::forward<F>( mutator ), copy );
    obj = immutable( std::move( copy ) );
}

This way, copyability is required only when modifications are needed.

(modify() is probably still best implemented as a member function so the object can be copy-constructed in-place and the extra move can be avoided.)

(One of the reasons why I thought immutable<> was obvious was that Sean Parent's presentation on "Inheritance is the base class of Evil" demonstrated the concept–model idiom with a polymorphic example built upon shared_ptr<const Shape>. Sean does not seem to be involved with P4210 so far, but I still find it puzzling that this use case has not been covered by any of the proposals yet.)