Revert "Adding locking around LoadFile in FileExternalAccountCredentials"

This reverts commit c51d063ff2.

src/core/lib/security/credentials/external/file_external_account_credentials.cc

@@ -102,11 +102,7 @@ void FileExternalAccountCredentials::RetrieveSubjectToken(
     std::function<void(std::string, grpc_error_handle)> cb) {
   // To retrieve the subject token, we read the file every time we make a
   // request because it may have changed since the last request.
-  absl::StatusOr<Slice> content_slice;
-  {
-    grpc_core::MutexLock l(&m_);
-    content_slice = LoadFile(file_, /*add_null_terminator=*/false);
-  }
+  auto content_slice = LoadFile(file_, /*add_null_terminator=*/false);
   if (!content_slice.ok()) {
     cb("", content_slice.status());
     return;

src/core/lib/security/credentials/external/file_external_account_credentials.h

@@ -52,7 +52,6 @@ class FileExternalAccountCredentials final : public ExternalAccountCredentials {
   std::string file_;
   std::string format_type_;
   std::string format_subject_token_field_name_;
-  grpc_core::Mutex m_;
 };
 
 }  // namespace grpc_core