The folks at Honda might beg to differ...That's easy. I'd take the 20 special purpose bots, or possibly a central computer controlling 20 special purpose remotes. The 20 special purpose bots, plus their control systems, are unlikely to be more expensive than the one generalist plus its control systems.
Building a generalist system is good for tasks that are done rarely. For tasks that are done frequently, a specialized tool usually does a better job, cheaper.
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The implication of the generalist bot isn't that the "only way to do dishes is in a sink", the implication is that when your bot is broken, something or someone has to do dishes. In all likelihood 'doing the dishes' is actually 'loading the dishwasher', which may contain any number of sensor and feedback systems to determine how clean the dishes are. IMHO the Jeeves-bot will probably be collecting dishes to load into a machine that could probably qualify as a bot in itself.
The generalist-bot doesn't actually need to be humaniform (vargriform? aslaniform?), but consider how many of the things in the world are already designed to be used by things of that shape?
IMTU it's pretty much moot anyway, there are plenty of people around who need jobs...