"Statistically though, on the evidence we have, it seems a tiny bit less safe than hospital birth".
Safer for whom? The evidence on neonatal outcomes is unreliable because of the overall safety of birth in or out of hospital (serious poor outcomes being rare).
What we do have when it comes to homebirth vs hospital birth is fairly good evidence that morbidity rates are lower for babies born at home - less fetal distress, and lower rates of admission to SCBU.
And for mums there's pretty solid evidence of better clinical outcomes - significantly lower rates of c/s, lower rates of instrumental birth, lower rates of episiotomy and lower rates of postnatal depression.
So really - can hospital birth be said to be even 'marginally safer' when it puts women at greater risk of needing emergency c/s, with all the risks (to the mother and to subsequent pregnancies) which accompany this type of surgery?
"Exactly but that is an argument for improving hositals so that women can have both the best in terms of safety and not needing to transfer AND a good experience wiht available pain relief"
You will never be able to create a hospital environment which offers similar benefits to homebirth. Doesn't matter how many birth pools you have or how many midwives. Hospitals are still, and will always be, large, protocol driven institutions where the needs of the individual will always have to come second to the smooth functioning of a medical system which is 'processing' huge numbers of women and babies every week.
Re: transfer from homebirth, women often give this as a reason not to have their baby at home. They assume it's one of the worst things which you can experience in labour. Having transferred in from a non-progressing homebirth myself, and knowing many other people who've done the same (including people who've had blue-light transfers) I have to say it's not usually anywhere near as bad as most people assume. And most women who do transfer in during labour are still glad they opted for a homebirth and many plan to try for a homebirth again the next time around.