The textarea does not display the placeholder on initial load. However if you focus on the textarea and blur it (e.g. click outside the textarea) the placeholder will appear.
Code snippet:
<Textarea
value={this.state.commentDraft}
placeholder="Write a comment..."
style={{ fontSize: 'small', maxHeight: '250px', resize: 'none' }}
onChange={e => this.setState({ commentDraft: e.target.value })} />
OS: Windows 10
Browser: IE 11