Earlier quoted context omitted.
While there maybe some truth to that, it's also worth noting that we see the same with all our (British) terrestrial TV networks. Particularly channel 4, which has given us classics such as The IT Crowd, Father Ted, The Inbetweeners and Black Books. Edit: and Brass Eye. How could I forgot Brass Eye when this topic is specifically about satire? Awesome show.
Let's regress this a level further - creating lots of small shows with potentially longer runs could result in a better talent pool (both actors/directors/producers), benefiting even private networks. How often do BBC actors work with other networks? If there's any cross-pollination there is an argument that the BBC's reach goes beyond it's own productions.
Since partial privatisation much of the BBC's output is actually commissioned through a maze of independents. It's not like the old days when Morcambe and Wise being poached to ITV was a national crisis.