I simply solved it with the indent() function:

xml.etree.ElementTree.indent(tree, space=" ", level=0) Appends whitespace to the subtree to indent the tree visually. This can be used to generate pretty-printed XML output. tree can be an Element or ElementTree. space is the whitespace string that will be inserted for each indentation level, two space characters by default. For indenting partial subtrees inside of an already indented tree, pass the initial indentation level as level.

tree = ET.ElementTree(root)
ET.indent(tree, space="\t", level=0)
tree.write(file_name, encoding="utf-8")

Note, the indent() function was added in Python 3.9.

import xml.dom.minidom

dom = xml.dom.minidom.parse(xml_fname) # or xml.dom.minidom.parseString(xml_string)
pretty_xml_as_string = dom.toprettyxml()

You can use the function toprettyxml() from xml.dom.minidom in order to do that:

def prettify(elem):
    """Return a pretty-printed XML string for the Element.
    """
    rough_string = ElementTree.tostring(elem, 'utf-8')
    reparsed = minidom.parseString(rough_string)
    return reparsed.toprettyxml(indent="\t")

The idea is to print your Element in a string, parse it using minidom and convert it again in XML using the toprettyxml function.

Source: http://pymotw.com/2/xml/etree/ElementTree/create.html

I was having issues using pretty print. Digging more into it I found the below solution which worked for me.

import xml.etree.cElementTree as etree
from xml.dom import minidom

root = etree.Element("root")
animal = etree.SubElement(root, "animal")
etree.SubElement(animal, "pet").text = "dog"

xmlstr = 
minidom.parseString(etree.toString(root)).toprettyxml(indent = "   ")
print (xmlstr)

Returns the result in XML format

Update: See xml.etree.ElementTree.indent as of Python 3.9.

I couldn't reproduce the bad indentation from your example, but according to http://effbot.org/zone/element-lib.htm#prettyprint, your function is mis-copied. For these lines:

if not elem.text or not elem.text.strip():
    elem.text = i + ""

There should be two space between the quotes:

if not elem.text or not elem.text.strip():
  elem.text = i + "  "

I ran this code and it displays properly.

from xml.etree import ElementTree as et

def indent(elem, level=0):
  i = "\n" + level*"  "
  if len(elem):
    if not elem.text or not elem.text.strip():
      elem.text = i + "  "
    if not elem.tail or not elem.tail.strip():
      elem.tail = i
    for e in elem:
      indent(e, level+1)
    if not e.tail or not e.tail.strip():
      e.tail = i
  else:
    if level and (not elem.tail or not elem.tail.strip()):
      elem.tail = i

data = '''<one><two><three>3</three><four>4</four></two></one>'''
tree = et.fromstring(data)
indent(tree)
et.dump(tree)

Output:

<one>
  <two>
    <three>3</three>
    <four>4</four>
  </two>
</one>

Notes for future:

• Images of text can't be copied so I leave it as an exercise for you to test on your own XML.
• Cut-n-paste exact code and input data as text to reproduce the issue to make it easy for answers to reproduce the issue.