Does this line of reasoning hold true for a dual-mono design with separate power supplies, transformers and heat sinks? Would impedance issues still be a factor?
Yes it does still hold true, although an amplifier like that may tend to be better able to tolerate the increased current.
It's pretty much a moot question, though, because if the amplifier isn't designed to be bridged it won't provide the phase inversion that is necessary.
Regarding paralleling, as opposed to bridging, the near zero output impedance of a solid state amp would cause essentially unlimited current to flow between the outputs of the two channels if for any reason their gains were to ever become significantly unequal, or if the input signal to one channel is ever absent for any reason. The result would stand a good chance of being a cloud of smoke. Presumably and hopefully the Mac and Bryston models NGJockey referred to have specific provisions in their designs to address those possibilities.
Tube amps are more likely to be capable of being paralleled, because their higher output impedance would provide some degree of current limiting in those kinds of situations. But I still wouldn't parallel a tube amp without a specific ok from the manufacturer, and I'm not sure I would do it even with an ok.
And since paralleling would provide a significant increase only with respect to current capability, and not with respect to voltage swing capability, its potential benefit would be limited to situations where the impedance characteristics of the speaker require more current than the amp can comfortably provide.
Best regards,
-- Al