Solar usually gets this criticism more than wind, so let's use that: the argument goes that you need enough power generating capacity to handle peak usage, but of course solar only works in the day. So if your peak usage happens at night (it doesn't, but let's assume) then the solar panels have "displaced zero power plants".
But who cares? If you have them built, then during the day the solar plants are operating and generating (much cheaper, looking only at marginal costs) power. And the coal and gas plants, by virtue of having higher marginal costs, are idle. And at night the fossil plants fire back up and do what they were doing before. So the net effect, assuming excess solar capacity, is that carbon output has been reduced by a factor of two (actually a bit more than two in practice).
And of course then the market will accomodate, such that "day power" being available in higher quantity and with higher excess capacity becomes cheaper and "night power" more expensive. So the legacy coal plants will probably still even make money as they're selling into a "premium" market.
So... how is solar (or wind) a toy in that scenario?