I's actually way less hassle than reusable nappies, and a lot less icky because you have a nice large wiping surface! Flannels are big enough that you are actually never at risk of pooey fingers, which has happened to me with wipes on a nasty change.
We have a nappy bucket, folded clean soft flannels in a pile in a wicker basket. When I change the baby I take one, dunk in a bowl of warm water (obviously you only ever dunk a clean, dry one in), then wipe the bottom, throw in nappy bucket. Then I pat the baby dry with another clean, dry flannel.The nappy bucket has a (close-fitting!) lid and I put a wash on at 75 degrees (70 degrees kills bacteria, so machine is fine) every other night. My kids have chronically sensitive skin, and they suffered when we go on holiday and I have to use wipes. Really bad rash inside 3 or 4 days, whatever the brand. As long as the flannels get washed in Surcare, along with all their clothes and bedlinen, they're fine.
It's a lot less hassle than using washable nappies because no stuffing pockets or worrying about liners. Literally just hot washing. I have an old towel I upend them into, grab corners and shove that into the machine, then use bleach wipes for the inside of the bucket before replacing it in the bathroom.
It's better for the baby, better for the environment, and you save an absolute fecking fortune. We use eco nappies (my two are allergic to everything else, up to and including washables) which are not exactly cheap, and if we had to pay Water Wipe prices too, we would have a whopping bill. Ikea multipack of white flannels - same as the old terry nappies, really - is £3 a pop. We have about 40, though I never use more than 10 a day now, but a newborn needs so many changes. All the face flannels are coloured, so no risk of confusion!
Though after boil washing my squeamishness is probably pretty stupid.
It's not for everyone, but as Water Wipes can cost you £15 a week if you use them for everything, and newborns need near constant changes, £12 all in plus some hot washes seems a reasonable deal to me.