problem is the attitude it may induce, which may be at such a rate that the automatics cannot deal with it and IAS reduces.
RifRaf3, concisely put.
Problem:
If one (the pilot, not the automatics) isn't actively engaged in attitude flying as things begin to go all wrong, then that old fashioned method of aviation that served us so well for so long when flying on instruments -- a working instrument scan and attitude/power flying -- has to be asserted into the control scheme by the meat based system. This will happen with a delay of "x" time by a crew that may have been, up until that point, watching the smart plane fly for them ... and it may not necessarily have been attitude flying while it was so doing.
Result? Flight deck crew begins the game of "catch up" if, as suggested above, the system logic finds itself in the wrong mode and starts to "gracefully degrade" to a less automated mode.
As much as FBW is not my personal cup of tea, this is not an inherently bad design philosophy -- auto degrading to keep the automatics from going utterly haywire -- but it is one that requires the meat based pilot to be "in the game" with the scan going when that degradation occurs. It also requires that the meat based system be very knowledgeable, in depth, about his complex system.