diff --git a/wgpu-core/src/device/queue.rs b/wgpu-core/src/device/queue.rs
index 8b1feefab..ba3974fa9 100644
--- a/wgpu-core/src/device/queue.rs
+++ b/wgpu-core/src/device/queue.rs
@@ -154,7 +154,10 @@ impl Drop for Queue {
             self.device.raw().wait(
                 fence.as_ref(),
                 last_successful_submission_index,
+                #[cfg(not(target_arch = "wasm32"))]
                 crate::device::CLEANUP_WAIT_MS,
+                #[cfg(target_arch = "wasm32")]
+                0, // WebKit and Chromium don't support a non-0 timeout
             )
         };
         drop(fence);
@@ -163,6 +166,13 @@ impl Drop for Queue {
             Ok(true) => {}
             // Note: If we don't panic here we are in UB land (destroying resources while they are still in use by the GPU).
             Ok(false) => {
+                // It's fine that we timed out on WebGL; GL objects can be deleted early as they
+                // will be kept around by the driver if GPU work hasn't finished.
+                // Moreover, the way we emulate read mappings on WebGL allows us to execute map_buffer earlier than on other
+                // backends since getBufferSubData is synchronous with respect to the other previously enqueued GL commands.
+                // Relying on this behavior breaks the clean abstraction wgpu-hal tries to maintain and
+                // we should find ways to improve this. See https://github.com/gfx-rs/wgpu/issues/6538.
+                #[cfg(not(target_arch = "wasm32"))]
                 panic!("We timed out while waiting on the last successful submission to complete!");
             }
             Err(e) => {
diff --git a/wgpu-hal/src/gles/device.rs b/wgpu-hal/src/gles/device.rs
index 0421adc04..27aabc51e 100644
--- a/wgpu-hal/src/gles/device.rs
+++ b/wgpu-hal/src/gles/device.rs
@@ -1563,6 +1563,10 @@ impl crate::Device for super::Device {
     ) -> Result<bool, crate::DeviceError> {
         if fence.last_completed.load(Ordering::Relaxed) < wait_value {
             let gl = &self.shared.context.lock();
+            // MAX_CLIENT_WAIT_TIMEOUT_WEBGL is:
+            // - 1s in Gecko https://searchfox.org/mozilla-central/rev/754074e05178e017ef6c3d8e30428ffa8f1b794d/dom/canvas/WebGLTypes.h#1386
+            // - 0 in WebKit https://github.com/WebKit/WebKit/blob/4ef90d4672ca50267c0971b85db403d9684508ea/Source/WebCore/html/canvas/WebGL2RenderingContext.cpp#L110
+            // - 0 in Chromium https://source.chromium.org/chromium/chromium/src/+/main:third_party/blink/renderer/modules/webgl/webgl2_rendering_context_base.cc;l=112;drc=a3cb0ac4c71ec04abfeaed199e5d63230eca2551
             let timeout_ns = if cfg!(any(webgl, Emscripten)) {
                 0
             } else {