Angular: radio button [checked] not set with template reference variable

As the title suggests, I have a scenario where, if the "Select All" radio button is checked, it must check all of the radio buttons in the columns below. Unfortunately, this is not working.

Here is a sample:

<table>
  <thead>
    <th>Role</th>
    <th colspan="3">Access</th>
  </thead>
  <tbody>
    <tr>
      <td>Select All</td>
      <td>
        <input #none type="radio" name="access0" value="allNone"/>
        <label>None</label>
      </td>
      <td>
        <input #readOnly type="radio" name="access0" value="allReadOnly"/>
        <label>Read Only</label>
      </td>
      <td>
        <input #full type="radio" name="access0" value="AllFull"/>
        <label>Full</label>
      </td>
    </tr>
    <tr>
      <td>Admin</td>
      <td>
        <input type="radio" name="access1" value="None" [checked]="none.checked"/>
        <label>None</label>
      </td>
      <td>
        <input type="radio" name="access1" value="ReadOnly" [checked]="readOnly.checked"/>
        <label>Read Only</label>
      </td>
      <td>
        <input type="radio" name="access1" value="Access" [checked]="full.checked"/>
        <label>Full</label>
      </td>
    </tr>
    <tr>
      <td>Sales Person</td>
      <td>
        <input type="radio" name="access2" value="None" [checked]="none.checked"/>
        <label>None</label>
      </td>
      <td>
        <input type="radio" name="access2" value="ReadOnly" [checked]="readOnly.checked"/>
        <label>Read Only</label>
      </td>
      <td>
        <input type="radio" name="access2" value="Access" [checked]="full.checked"/>
        <label>Full</label>
      </td>
    </tr>
  </tbody>
</table>

And here is a link to a sample StackBlitz.

I am not sure why, for instance, all of the 'None' radio buttons are not checked when setting the [checked] as follow:

<input type="radio" name="access1" value="None" [checked]="none.checked"/>

Check for changes:

<table (click)="cd.detectChanges()">
    <thead>
        <th>Role</th>
        <th colspan="3">Access</th>
    </thead>
    <tbody>
        <tr>
            <td>Select All</td>
            <td>
                <input #none type="radio" name="access0" value="allNone"/>
        <label>None</label>
      </td>
      <td>
        <input #readOnly type="radio" name="access0" value="allReadOnly"/>
        <label>Read Only</label>
      </td>
      <td>
        <input #full type="radio" name="access0" value="AllFull"/>
        <label>Full</label>
      </td>
    </tr>
    <tr>
      <td>Admin</td>
      <td>
        <input type="radio" name="access1" [value]="None" [checked]="none.checked"/>
        <label>None</label>
      </td>
      <td>
        <input type="radio" name="access1" value="ReadOnly" [checked]="readOnly.checked"/>
        <label>Read Only</label>
      </td>
      <td>
        <input type="radio" name="access1" value="Access" [checked]="full.checked"/>
        <label>Full</label>
      </td>
    </tr>
    <tr>
      <td>Sales Person</td>
      <td>
        <input type="radio" name="access2" value="None" [checked]="none.checked"/>
        <label>None</label>
      </td>
      <td>
        <input type="radio" name="access2" value="ReadOnly" [checked]="readOnly.checked"/>
        <label>Read Only</label>
      </td>
      <td>
        <input type="radio" name="access2" value="Access" [checked]="full.checked"/>
        <label>Full</label>
      </td>
    </tr>
  </tbody>
</table>

And TS:

import {ChangeDetectorRef, Component} from '@angular/core';

@Component({
  selector: 'my-app',
  templateUrl: './app.component.html',
  styleUrls: [ './app.component.css' ]
})
export class AppComponent  {
  constructor(protected cd: ChangeDetectorRef){}
}