diff --git a/winit-core/Cargo.toml b/winit-core/Cargo.toml
index 0b9dd9e621..bce82c983b 100644
--- a/winit-core/Cargo.toml
+++ b/winit-core/Cargo.toml
@@ -23,11 +23,9 @@ rwh_06.workspace = true
 serde = { workspace = true, optional = true }
 smol_str.workspace = true
 
-[target.'cfg(target_family = "wasm")'.dependencies]
+# `wasm32-unknown-unknown` and `wasm32-none`, but not `wasm32-wasi`.
+[target.'cfg(all(target_family = "wasm", any(target_os = "unknown", target_os = "none")))'.dependencies]
 web-time.workspace = true
 
-[build-dependencies]
-cfg_aliases.workspace = true
-
 [dev-dependencies]
 winit.workspace = true
diff --git a/winit-core/build.rs b/winit-core/build.rs
deleted file mode 100644
index 915ec231b8..0000000000
--- a/winit-core/build.rs
+++ /dev/null
@@ -1,11 +0,0 @@
-use cfg_aliases::cfg_aliases;
-
-fn main() {
-    // The script doesn't depend on our code.
-    println!("cargo:rerun-if-changed=build.rs");
-
-    // Setup cfg aliases.
-    cfg_aliases! {
-        web_platform: { all(target_family = "wasm", target_os = "unknown") },
-    }
-}
diff --git a/winit-core/src/event.rs b/winit-core/src/event.rs
index 416723749c..42c37c8d1c 100644
--- a/winit-core/src/event.rs
+++ b/winit-core/src/event.rs
@@ -1,15 +1,11 @@
 //! The event enums and assorted supporting types.
 use std::path::PathBuf;
 use std::sync::{Mutex, Weak};
-#[cfg(not(web_platform))]
-use std::time::Instant;
 
 use dpi::{PhysicalPosition, PhysicalSize};
 #[cfg(feature = "serde")]
 use serde::{Deserialize, Serialize};
 use smol_str::SmolStr;
-#[cfg(web_platform)]
-use web_time::Instant;
 
 use crate::error::RequestError;
 use crate::event_loop::AsyncRequestSerial;
@@ -17,6 +13,7 @@ use crate::keyboard::{self, ModifiersKeyState, ModifiersKeys, ModifiersState};
 #[cfg(doc)]
 use crate::window::Window;
 use crate::window::{ActivationToken, Theme};
+use crate::Instant;
 
 /// Describes the reason the event loop is resuming.
 #[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
diff --git a/winit-core/src/event_loop/mod.rs b/winit-core/src/event_loop/mod.rs
index 8d35b1180b..71307ee7c2 100644
--- a/winit-core/src/event_loop/mod.rs
+++ b/winit-core/src/event_loop/mod.rs
@@ -4,18 +4,16 @@ pub mod run_on_demand;
 use std::fmt::{self, Debug};
 use std::sync::atomic::{AtomicUsize, Ordering};
 use std::sync::Arc;
-#[cfg(not(web_platform))]
-use std::time::{Duration, Instant};
+use std::time::Duration;
 
 use rwh_06::{DisplayHandle, HandleError, HasDisplayHandle};
-#[cfg(web_platform)]
-use web_time::{Duration, Instant};
 
 use crate::as_any::AsAny;
 use crate::cursor::{CustomCursor, CustomCursorSource};
 use crate::error::RequestError;
 use crate::monitor::MonitorHandle;
 use crate::window::{Theme, Window, WindowAttributes};
+use crate::Instant;
 
 pub trait ActiveEventLoop: AsAny + fmt::Debug {
     /// Creates an [`EventLoopProxy`] that can be used to dispatch user events
diff --git a/winit-core/src/event_loop/run_on_demand.rs b/winit-core/src/event_loop/run_on_demand.rs
index a6e225623f..4fa5a019b0 100644
--- a/winit-core/src/event_loop/run_on_demand.rs
+++ b/winit-core/src/event_loop/run_on_demand.rs
@@ -32,13 +32,7 @@ pub trait EventLoopExtRunOnDemand {
     /// # Caveats
     /// - This extension isn't available on all platforms, since it's not always possible to return
     ///   to the caller (specifically this is impossible on iOS and Web - though with the Web
-    ///   backend it is possible to use
-    #[cfg_attr(
-        web_platform,
-        doc = "  [`EventLoopExtWeb::spawn_app()`][crate::platform::web::EventLoopExtWeb::spawn_app()]"
-    )]
-    #[cfg_attr(not(web_platform), doc = "  `EventLoopExtWeb::spawn_app()`")]
-    ///   [^1] more than once instead).
+    ///   backend it is possible to use `EventLoopExtWeb::spawn_app()`[^1] more than once instead).
     /// - No [`Window`] state can be carried between separate runs of the event loop.
     ///
     /// You are strongly encouraged to use [`EventLoop::run_app()`] for portability, unless you
diff --git a/winit-core/src/keyboard.rs b/winit-core/src/keyboard.rs
index 156a32d4ad..22fbe29480 100644
--- a/winit-core/src/keyboard.rs
+++ b/winit-core/src/keyboard.rs
@@ -1560,9 +1560,9 @@ impl NamedKey {
     /// # Examples
     ///
     /// ```
-    /// # #[cfg(web_platform)]
+    /// # #[cfg(target_family = "wasm")]
     /// # wasm_bindgen_test::wasm_bindgen_test_configure!(run_in_browser);
-    /// # #[cfg_attr(web_platform, wasm_bindgen_test::wasm_bindgen_test)]
+    /// # #[cfg_attr(target_family = "wasm", wasm_bindgen_test::wasm_bindgen_test)]
     /// # fn main() {
     /// use winit_core::keyboard::NamedKey;
     ///
@@ -1587,9 +1587,9 @@ impl Key {
     /// # Examples
     ///
     /// ```
-    /// # #[cfg(web_platform)]
+    /// # #[cfg(target_family = "wasm")]
     /// # wasm_bindgen_test::wasm_bindgen_test_configure!(run_in_browser);
-    /// # #[cfg_attr(web_platform, wasm_bindgen_test::wasm_bindgen_test)]
+    /// # #[cfg_attr(target_family = "wasm", wasm_bindgen_test::wasm_bindgen_test)]
     /// # fn main() {
     /// use winit_core::keyboard::{Key, NamedKey};
     ///
diff --git a/winit-core/src/lib.rs b/winit-core/src/lib.rs
index 358f0c3a6f..89bc682164 100644
--- a/winit-core/src/lib.rs
+++ b/winit-core/src/lib.rs
@@ -19,3 +19,11 @@ pub mod icon;
 pub mod keyboard;
 pub mod monitor;
 pub mod window;
+
+// `Instant` is not actually available on `wasm32-unknown-unknown`, the `std` implementation there
+// is a stub. And `wasm32-none` doesn't even have `std`. Instead, we use `web_time::Instant`.
+#[cfg(not(all(target_family = "wasm", any(target_os = "unknown", target_os = "none"))))]
+pub(crate) use std::time::Instant;
+
+#[cfg(all(target_family = "wasm", any(target_os = "unknown", target_os = "none")))]
+pub(crate) use web_time::Instant;