I don't really see how anyone could think there'd be a reduction in box count. Minimum required is one 'control box', 5 speakers and a sub. Whether the power amplification is in the 'control box' or speakers it all works out the same. As The_Lhc said it's only if you have separate pre/pro and multichannel power that you'd get a reduction and even then only by one.
There's no reason in principle why active should be any more difficult (save the odd power cable) or expensive than a passive 5.1 setup. However, the global market in AVRs dwarfs two channel and active speakers, thus competition means AVRs represent great value. You get high quality amplification and an excellent feature set for rock bottom prices (at whatever level you go in at).
Happily, there are now a number of options for reasonably priced pre pros coming in from the US (and even the audiolab is more reasonable than has traditionally been available). Carefully chosen, a £300 pre pro and £3k active setup ought to compete (at least) with a £1k AVR and £2-2.5k passive speaker setup.
I am not, however, aware of any reasonably priced dedicated active centre speakers (I stand to be corrected). Also, for real value for money you are going to have to consider pro styled actives; the selection of active speakers in this price range with domestic finishes is pretty small.