Count query optimization code only checks $this->groupby and not presence of "aggregate" fields

I don't know if this is a bug, so I submit it as support request.
My handler does aggregation by adding field with "aggregate" = TRUE property (and NOT invoking add_groupby()). This breaks count queries, because query() method only checks if there are GROUP BY clauses by checking $this->groupby. It doesn't check if there are aggregate fields.
It doesn't find $this->groupby, and tries to optimize the query leaving only base field (and counting it).
I.e. it's the following code block:

/**
     * An optimized count query includes just the base field instead of all the fields.
     * Determine of this query qualifies by checking for a groupby or distinct.
     */
    $fields_array = $this->fields;
    if ($get_count && !$this->groupby) {
      foreach ($fields_array as $field) {
        if (!empty($field['distinct'])) {
          $get_count_optimized = FALSE;
          break;
        }
      }
    }
    else {
      $get_count_optimized = FALSE;
    }
    if (!isset($get_count_optimized)) {
      $get_count_optimized = TRUE;
    }

First question: shouldn't it also check presence of "aggregate" fields and set $get_count_optimized = FALSE too ?
Second question: is it a bug of Views that query() method gets $this->groupby empty when there are "aggregate" fields ?

Other than paging, the view is working fine. So this provides third question: should handlers also invoke add_groupby() when adding "aggregate" fields ? If that is the case it's not convenient because if handler doesn't run last, it can't know other fields participating in the query so it can't cast GROUP BY on them.
I know that I can manually feed proper count query by using hook_views_pre_execute() but that's inconvenient too and ties your code to specific views.