The benefit of not having the placenta jab is not having to have an injection :o If I'd had an epidural maybe I would have had it because I wouldn't have been able to feel it. But then again I tend to get lingering pain at injection sites so I might have said no anyway.
After birth I was really incredibly antsy and wet about people touching me/doing things to me and particularly anything that hurt, like a needle. I needed stitches for my first birth and I whined so much about it even after 4 local anaesthetic injections I think the doctor wanted to tell me to get a grip 
then for the third they were looking for ages to try and work out if I'd torn or not and I was insistent that I hadn't and they should stop (they didn't; I hadn't). Second was fine but they basically left me alone as DS2 had breathing issues so they were more worried about him. Also with the third, they subjected me to the bastard that is fundal massage at that birth which I was very very pissed off about and complained about a lot - (this was in Germany, I know it's not standard practice in the UK).
Also this (sorry Shloer, I don't mean to single you out, you just have interesting points to respond to)
I don’t know a single person who hasn’t accepted pain relief for operations, appendixes being removed, broken legs etc.
This is absolutely true - but I don't see it as the same situation at all.
When you have an operation it's a very calm, planned event and you are able to reasonably know pretty much exactly how it will go beforehand so it's easy to make decisions and weigh up different options for pain relief. For example I severed a tendon in my finger and was able to choose local or general. Also it is generally quite important that you stay still and aren't thrashing around and screaming with pain :o so some kind of pain relief is useful for that. Labour isn't something being done to you, it's something that you are doing so you don't really need to stay still. In fact it can quite often help if you don't.
On the other end of the scale a broken leg is an emergency, and I'd be making my way to hospital ASAP and after any pain relief as soon as it was available. Also, unlike labour the pain won't go away until the injury is fixed (and even then not immediately). When you give birth the pain pretty much stops as soon as the baby is out, and that will happen at some point (or else you'll have pain relief for whatever procedure is used to help the baby out). So it is an option, albeit not a very comfortable one, just to wait it out.
In labour, there's a really long drawn out bit where you're coping at home without any pain relief options at all. They won't even GIVE you the pain relief until you're really into labour and it's well established etc - by which time you have already been coping with it for several hours using whatever methods and the pain relief options you have all have various downsides. Epidural is meant to be the bees knees but you've got to be absolutely still and calm and listening to instructions while they insert it and it's also not like you can ask for it and then instantly get it. You have to ask for it and then they have to notify the anaesthetist and you have to wait for them to be free and then wait for them to come into the room and introduce themselves and if you haven't done the paperwork in advance you have to do it then and there, and they often want you on a monitor for a bit if not for the whole time, all of this while contracting and all that time you can't use any of the other stuff that really helps such as vigorous movement or being in water or just kind of somehow going into a deep inner space (which is so absolutely not me, but somehow something I did in births #1 and #3 at least for part of it in the middle). And then when you get it you can't move around which is a bit freaky (though I'm 100% sure I wouldn't care about this if it took the labour pain away). But there is also a chance it won't work or will only partially work which seems like a massive gamble.
Opiates seem nice and easy to get, and at some point the labour pains definitely outweigh fear of needles, but I was a bit wary of the fact that you can't have them too close to the end of labour so basically just at the point the contractions are getting unmanageably strong it has to wear off, and then you can't have any more but you also might not have any coping mechanisms because you haven't been doing them for the last 4 hours or however long it lasts. TBH the thought of it going away and then coming back and starting again is absolutely terrifying, much worse than it just keeping going without a break. If I ever had twins I would absolutely have opted for a c-section as I can't imagine anything worse than crowning and then having a break knowing you have to go through crowning again in a few minutes' time! Although I liked the idea of a "pethidine rest" where they give you something like that so you can sleep/relax/recharge during a really long drawn out labour before the pains get to the insane level - mine were like that, although it wasn't something I was offered.
Gas and air was lovely but I liked it much better in the UK. In Germany it was treated as this overtly medical thing so I wasn't allowed to have it in the pool, I had to be on two different kinds of monitor and I was put on a bed on my back and I couldn't be arsed to argue with them at that point, I just cooperated to get the drugs and then the thought of getting down was just too complicated so I carried on up there. I did consider having an epidural at that point, but to be totally honest the idea of having to wait for the anaesthetist was killing me so I went with the instant gas and that was about enough until the end.
It wasn't really that I didn't want pain relief in my labours, but that the process to get the pain relief seemed to be quite complicated and actually it sort of helped more just to try and focus on getting through the contractions until the point that they became unmanageable.