BrowserTestBase does not work with standard profile

As soon as you set "protected $profile = 'standard';" on a browser test it blows up with:

Drupal\FunctionalTests\BrowserTest\StandardProfileTest::testStandardProfile
PHPUnit_Framework_Exception: PDOException: SQLSTATE[42S02]: Base table or view not found: 1146 Table 'drupal-8.simpletest422195search_total' doesn't exist in core/lib/Drupal/Core/Database/Statement.php:59
Stack trace:
#0 core/lib/Drupal/Core/Database/Statement.php(59): PDOStatement->execute(Array)
#1 core/lib/Drupal/Core/Database/Connection.php(610): Drupal\Core\Database\Statement->execute(Array, Array)
#2 core/lib/Drupal/Core/Database/Driver/mysql/Connection.php(81): Drupal\Core\Database\Connection->query('SELECT t.word A...', Array, Array)
#3 core/includes/database.inc(61): Drupal\Core\Database\Driver\mysql\Connection->query('SELECT t.word A...', Array, Array)
#4 core/modules/search/search.module(220): db_query('SELECT t.word A...', Array, Array)
#5 core/includes/bootstrap.inc(978): search_update_totals()
#6 [internal function]: _drupal_shutdown_function()
#7 {main}

Next Drupal\Core\Database\DatabaseExceptionWrapper: SQLSTATE[42S02]: Base table or view not found: 1146 Table 'drupal-8.simpletest422195search_total' doesn't exist: SELECT t.word AS realword, i.word FROM {search_total} t LEFT JOIN {search_index} i ON t.word = i.word WHERE i.word IS NULL; Array
(
)
 in core/lib/Drupal/Core/Database/Connection.php:671
Stack trace:
#0 core/lib/Drupal/Core/Database/Connection.php(635): Drupal\Core\Database\Connection->handleQueryException(Object(PDOException), 'SELECT t.word A...', Array, Array)
#1 core/lib/Drupal/Core/Database/Driver/mysql/Connection.php(81): Drupal\Core\Database\Connection->query('SELECT t.word A...', Array, Array)
#2 core/includes/database.inc(61): Drupal\Core\Database\Driver\mysql\Connection->query('SELECT t.word A...', Array, Array)
#3 core/modules/search/search.module(220): db_query('SELECT t.word A...', Array, Array)
#4 core/includes/bootstrap.inc(978): search_update_totals()
#5 [internal function]: _drupal_shutdown_function()
#6 {main}

We should add a test for that and make sure it works.