diff --git a/core/modules/content_translation/tests/src/Functional/ContentTranslationEnableTest.php b/core/modules/content_translation/tests/src/Functional/ContentTranslationEnableTest.php
index 097cd05a58a0c75bb9d64b2970af0ad69eccade4..edbbfe990fa34c657fb925c18409e4d97688df09 100644
--- a/core/modules/content_translation/tests/src/Functional/ContentTranslationEnableTest.php
+++ b/core/modules/content_translation/tests/src/Functional/ContentTranslationEnableTest.php
@@ -5,6 +5,7 @@
 namespace Drupal\Tests\content_translation\Functional;
 
 use Drupal\Tests\BrowserTestBase;
+use Drupal\user\Entity\Role;
 
 /**
  * Test enabling content translation module.
@@ -20,14 +21,6 @@ class ContentTranslationEnableTest extends BrowserTestBase {
    */
   protected static $modules = ['entity_test', 'menu_link_content', 'node'];
 
-  /**
-   * {@inheritdoc}
-   *
-   * @todo Remove and fix test to not rely on super user.
-   * @see https://www.drupal.org/project/drupal/issues/3437620
-   */
-  protected bool $usesSuperUserAccessPolicy = TRUE;
-
   /**
    * {@inheritdoc}
    */
@@ -37,6 +30,11 @@ class ContentTranslationEnableTest extends BrowserTestBase {
    * Tests that entity schemas are up-to-date after enabling translation.
    */
   public function testEnable(): void {
+    $this->rootUser = $this->drupalCreateUser([
+      'administer modules',
+      'administer site configuration',
+      'administer content types',
+    ]);
     $this->drupalLogin($this->rootUser);
     // Enable modules and make sure the related config entity type definitions
     // are installed.
@@ -46,6 +44,7 @@ public function testEnable(): void {
     ];
     $this->drupalGet('admin/modules');
     $this->submitForm($edit, 'Install');
+    $this->rebuildContainer();
 
     // Status messages are shown.
     $this->assertSession()->statusMessageContains('This site has only a single language enabled. Add at least one more language in order to translate content.', 'warning');
@@ -55,6 +54,10 @@ public function testEnable(): void {
     $this->drupalGet('admin/reports/status');
     $this->assertSession()->elementTextEquals('css', "details.system-status-report__entry summary:contains('Entity/field definitions') + div", 'Up to date');
 
+    $this->grantPermissions(Role::load(Role::AUTHENTICATED_ID), [
+      'administer content translation',
+      'administer languages',
+    ]);
     $this->drupalGet('admin/config/regional/content-language');
     // The node entity type should not be an option because it has no bundles.
     $this->assertSession()->responseNotContains('entity_types[node]');
diff --git a/core/modules/content_translation/tests/src/Functional/ContentTranslationNewTranslationWithExistingRevisionsTest.php b/core/modules/content_translation/tests/src/Functional/ContentTranslationNewTranslationWithExistingRevisionsTest.php
index 7a8955a262ebc714ca834693bcbaa80097cebf8f..65f0c5ed4dc4cc07c1f2c84f0f6e3b41cfd4bb68 100644
--- a/core/modules/content_translation/tests/src/Functional/ContentTranslationNewTranslationWithExistingRevisionsTest.php
+++ b/core/modules/content_translation/tests/src/Functional/ContentTranslationNewTranslationWithExistingRevisionsTest.php
@@ -25,14 +25,6 @@ class ContentTranslationNewTranslationWithExistingRevisionsTest extends ContentT
     'node',
   ];
 
-  /**
-   * {@inheritdoc}
-   *
-   * @todo Remove and fix test to not rely on super user.
-   * @see https://www.drupal.org/project/drupal/issues/3437620
-   */
-  protected bool $usesSuperUserAccessPolicy = TRUE;
-
   /**
    * {@inheritdoc}
    */
diff --git a/core/modules/content_translation/tests/src/Functional/ContentTranslationOutdatedRevisionTranslationTest.php b/core/modules/content_translation/tests/src/Functional/ContentTranslationOutdatedRevisionTranslationTest.php
index 96726c68756ad96db338056490dc0e337276dddc..731ffd374c710d480911795cbdeda1f859df1af2 100644
--- a/core/modules/content_translation/tests/src/Functional/ContentTranslationOutdatedRevisionTranslationTest.php
+++ b/core/modules/content_translation/tests/src/Functional/ContentTranslationOutdatedRevisionTranslationTest.php
@@ -14,14 +14,6 @@
  */
 class ContentTranslationOutdatedRevisionTranslationTest extends ContentTranslationPendingRevisionTestBase {
 
-  /**
-   * {@inheritdoc}
-   *
-   * @todo Remove and fix test to not rely on super user.
-   * @see https://www.drupal.org/project/drupal/issues/3437620
-   */
-  protected bool $usesSuperUserAccessPolicy = TRUE;
-
   /**
    * {@inheritdoc}
    */
diff --git a/core/modules/content_translation/tests/src/Functional/ContentTranslationPendingRevisionTestBase.php b/core/modules/content_translation/tests/src/Functional/ContentTranslationPendingRevisionTestBase.php
index cd31802a13f05fcc20d00885e28a7705277f99df..24fd851abea7d8b02e8a369cd71b4497fdb5d2d1 100644
--- a/core/modules/content_translation/tests/src/Functional/ContentTranslationPendingRevisionTestBase.php
+++ b/core/modules/content_translation/tests/src/Functional/ContentTranslationPendingRevisionTestBase.php
@@ -79,6 +79,11 @@ protected function setUp(): void {
    * Enables content moderation for the test entity type and bundle.
    */
   protected function enableContentModeration() {
+    $perms = array_merge(parent::getAdministratorPermissions(), [
+      'administer workflows',
+      'view latest version',
+    ]);
+    $this->rootUser = $this->drupalCreateUser($perms);
     $this->drupalLogin($this->rootUser);
     $workflow_id = 'editorial';
     $this->drupalGet('/admin/config/workflow/workflows');
diff --git a/core/modules/content_translation/tests/src/Functional/ContentTranslationRevisionTranslationDeletionTest.php b/core/modules/content_translation/tests/src/Functional/ContentTranslationRevisionTranslationDeletionTest.php
index 8ecd28de8fe402fe1c0d07043b2b0164bebef73e..3e123a5ca4feabf981c3ce4a5b64359d45076ed9 100644
--- a/core/modules/content_translation/tests/src/Functional/ContentTranslationRevisionTranslationDeletionTest.php
+++ b/core/modules/content_translation/tests/src/Functional/ContentTranslationRevisionTranslationDeletionTest.php
@@ -14,14 +14,6 @@
  */
 class ContentTranslationRevisionTranslationDeletionTest extends ContentTranslationPendingRevisionTestBase {
 
-  /**
-   * {@inheritdoc}
-   *
-   * @todo Remove and fix test to not rely on super user.
-   * @see https://www.drupal.org/project/drupal/issues/3437620
-   */
-  protected bool $usesSuperUserAccessPolicy = TRUE;
-
   /**
    * {@inheritdoc}
    */
diff --git a/core/modules/content_translation/tests/src/Functional/ContentTranslationUntranslatableFieldsTest.php b/core/modules/content_translation/tests/src/Functional/ContentTranslationUntranslatableFieldsTest.php
index d0b8a15e1f83e29f64e91913d27dc742067e7114..02945baf525a1610d1a61754271624b73ea8d51b 100644
--- a/core/modules/content_translation/tests/src/Functional/ContentTranslationUntranslatableFieldsTest.php
+++ b/core/modules/content_translation/tests/src/Functional/ContentTranslationUntranslatableFieldsTest.php
@@ -24,14 +24,6 @@ class ContentTranslationUntranslatableFieldsTest extends ContentTranslationPendi
    */
   protected static $modules = ['field_test'];
 
-  /**
-   * {@inheritdoc}
-   *
-   * @todo Remove and fix test to not rely on super user.
-   * @see https://www.drupal.org/project/drupal/issues/3437620
-   */
-  protected bool $usesSuperUserAccessPolicy = TRUE;
-
   /**
    * {@inheritdoc}
    */