This single study being the largest one carried out in the UK, covering tens of thousands of births. If you want to dispute its findings then feel free to point to opposing data.

Looking at the data for second children:
For multiparous women, there were no significant differences in adverse perinatal outcomes between planned home births or midwifery unit births and planned births in obstetric units.

For multiparous women, birth in a non-obstetric unit setting significantly and substantially reduced the odds of having an intrapartum caesarean section, instrumental delivery or episiotomy.

So your outcomes are as good at home, and the odds of you not being sliced open are better.

https://www.npeu.ox.ac.uk/birthplace/results