I agree with you on the gas peakers comment.

Peaking power plants are typically used to provide the extra electricity needed when the supply of renewables start to fall off in the evening and the increased demand from HVAC and other loads coincide. They ramp fast (or start in a spinning reserve mode) to supply power in 5 to 10 mins. Nuclear plans can ramp but they're not really designed to ramp to replace all of the gas peakers.

Another issue is that the grid requires a certain amount of connected inertia in order to resist changes in frequency. Imbalance between generation and loads will lead to frequency changes. Frequency changes can affect motors, fans, negatively (over fluxing leading to premature failure), so there are typically protection systems that disconnect loads or generation outside of a nominal frequency band. Renewables compound this problem because they are variable (generation fluctuates), and because they are inverter based and provide no physical inertia. Therefore, as you increase renewables only, you see greater problems with frequency stability.

To combat the frequency issues today, you use more agile generators (typically gas) that can provide some inertia but also do fast power changes to arrest changes in frequency and restore system frequency (see primary frequency response).

It's hard to see how turning off all gas and displace it with nuclear will work unless you expect nuclear to provide all of the primary frequency response, which includes needing to both increase AND reduce power to stabilize frequency. Large nuclear plants with high inertia generators on their steam turbines do help keep frequency more stiff though, so that's helpful.

If you were to use nuclear to replace gas, you'd also need to make them fast ramping to manage variable renewables. Or you could retain some gas to be the variable load management units, but then you'd basically be keeping gas peakers.

Alternatively, if there is greater adoption of energy storage to help make renewables more dispatchable with more predictable power, that solves part of the frequency issue. I believe gas peakers typically run for under 4 hours a day, so 4 hour duration energy storage would be effective at retiring a lot of the gas except for that kept available as emergency power plants during disasters or weather events.

Part of the frequency and inertia problem will also get solved in the next decade or so. Generators provide an electrical response to the rate of change of frequency that serves to stabilize frequency called the inertial response. Essentially, the change in kinetic energy from one rotational velocity to a lower one results in an uncommanded power injection into the grid. This power injection then counteracts the lack of generation that led to the initial drop of frequency. Inverters are starting to get deployed with grid forming capability in which they can provide synthetic inertia, and over the next decade could reduce the need for synchronous inertia.

It's not an easy problem to solve so I always take sweeping recommendations with a grain of salt.

(I have been doing control system design for gas turbines, batteries, and renewable/thermal/battery hybrid systems for 15 years).