Appending HTML string to the DOM

Performance

AppendChild (E) is more than 2x faster than other solutions on chrome and safari, insertAdjacentHTML(F) is fastest on firefox. The innerHTML= (B) (do not confuse with += (A)) is second fast solution on all browsers and it is much more handy than E and F.

Details

Set up environment (2019.07.10) MacOs High Sierra 10.13.4 on Chrome 75.0.3770 (64-bit), Safari 11.1.0 (13604.5.6), Firefox 67.0.0 (64-bit)

• on Chrome E (140k operations per second) is fastest, B (47k) and F (46k) are second, A (332) is slowest
• on firefox F (94k) is fastest, then B(80k), D (73k), E(64k), C (21k) slowest is A(466)
• on Safari E(207k) is fastest, then B(89k), F(88k), D(83k), C (25k), slowest is A(509)

You can replay test in your machine here

function A() {    
  container.innerHTML += '<p>A: Just some <span>text</span> here</p>';
}

function B() {    
  container.innerHTML = '<p>B: Just some <span>text</span> here</p>';
}

function C() {    
  $('#container').append('<p>C: Just some <span>text</span> here</p>');
}

function D() {
  var p = document.createElement("p");
  p.innerHTML = 'D: Just some <span>text</span> here';
  container.appendChild(p);
}

function E() {    
  var p = document.createElement("p");
  var s = document.createElement("span"); 
  s.appendChild( document.createTextNode("text ") );
  p.appendChild( document.createTextNode("E: Just some ") );
  p.appendChild( s );
  p.appendChild( document.createTextNode(" here") );
  container.appendChild(p);
}

function F() {    
  container.insertAdjacentHTML('beforeend', '<p>F: Just some <span>text</span> here</p>');
}

A();
B();
C();
D();
E();
F();

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>

This snippet only for show code used in test (in jsperf.com) - it not perform test itself. 
<div id="container"></div>

Use insertAdjacentHTML which is supported in all current browsers:

div.insertAdjacentHTML( 'beforeend', str );

The position parameter beforeend will add inside the element, after its last child.

Live demo: http://jsfiddle.net/euQ5n/

Is this acceptable?

var child = document.createElement('div');
child.innerHTML = str;
child = child.firstChild;
document.getElementById('test').appendChild(child);

jsFiddle.

But, Neil's answer is a better solution.

The idea is to use innerHTML on an intermediary element and then move all of its child nodes to where you really want them via appendChild.

var target = document.getElementById('test');
var str = '<p>Just some <span>text</span> here</p>';

var temp = document.createElement('div');
temp.innerHTML = str;
while (temp.firstChild) {
  target.appendChild(temp.firstChild);
}

This avoids wiping out any event handlers on div#test but still allows you to append a string of HTML.