According to that same page, most natural gas plants currently in use utilize a combined cycle system which takes significantly longer than more flexible, but less prevalent, combustion turbines.

Though maybe the point is moot: Even if the total environmental impact of natural gas is the same as oil, and leaving aside the geopolitical issues-- natural gas is still cheaper, so if you're going to choose between two bad options then you might as well go with the lower cost one. At which point you just invest in upgrading those combined gas plants to more flexible combustion turbines.

However, nuclear isn't completely out of the game here: It may have a very long cold-start time, but in the last decade there's been progress in making it capable of load-following instead of just baseload, especially when it's planned, e.g after sunset. There's certainly other environmental factors there, but if we're worried about decreasing CO2 ASAP, nuclear should probably be part of the conversation.

An underutilized nuclear plant may still be a necessity instead of a luxury if we're running out of time on CO2 emissions. In this case, making economic sense may run counter to long term human interests.

Many are built to operate < 10% of capacity, so simple single stage instead of more efficient CCGT, because it's insanely cheap peak power compared to alternatives.