"Spinning reserve" is required whether you have zero renewable energy or 50% renewable energy. Those conventional plants that are in standby mode are required anyway, and adding renewables doesn't mean more are needed in standby mode. Additionally, modern gas stations can come online extremely quickly - basically, a modern gas station is the core of a Rolls Royce Trent jet engine, and it can throttle up in a power station just as rapidly as it can on a plane on its takeoff roll (in seconds. Of course the power turbine might take a bit longer, but it's measured in at most a few minutes).
In fact, from the point of view of the UK national grid, nuclear or coal power is seen as intermittent and wind power is seen as reliable. The reason is that Sizewell B (a very large nuclear power plant) can suddenly go offline without any warning at all, and suddenly the grid is short of 420MW. However, over a period of an hour, wind and solar are considered extremely reliable. We can easily predict what the wind is going to do over the next hour or so, it won't suddenly start or stop unforecast over a gigantic area. Also wind and solar plants are widely distributed and small. If a wind turbine suddenly goes offline you lose maybe 1MW out of 2GW of power production. So you actually need less spinning reserve for renewables than you do for a large nuclear or coal station because you don't risk suddenly losing all 420MW in an instant like you do with a large power station. Similarly, with solar, you can easily see where the storms are so you can easily predict how the generation is going to change over the next hour.
There isn't just spinning reserve either, high power users like electric furnaces have frequency cutoffs in them. On the UK national grid, when generating capacity is falling behind load, the frequency falls (and conversely, when the load is lighter than capacity, the frequency rises. IIRC they try to keep the frequency between something like 49.9Hz and 50.1Hz). Some industrial users who have equipment that takes days to get up to temperature aren't affected by having the power cut off for a half hour to this piece of equipment, so their contract with National Grid includes a piece of equipment that cuts the power to the equipment if the frequency falls below a certain threshold. This can be used for brief periods of load shedding.
So in summary, no, this is not an issue with solar and wind. The spinning reserve is required anyway, and from the point of view of the grid and the timescales for spinning reserve, wind and solar is actually seen as more reliable than a large coal or nuclear power station because of its distributed nature and the predictability of wind and solar over the short term.