Yes the alternatives for the seasonal storage problem are...fossil fuels. So obviously if we can't solve the seasonal problem yet with batteries, current battery tech isn't capable enough to make clean energy a reality without Nuclear.

Also, China's energy mix is irrelevant for Europe, the two regions have vastly different climates, population distributions, and government.

Europe has much bigger seasonal gaps in the winter for things like solar; Hydro is huge in China due to massive river systems like the Yangtze, but basically tapped out in Europe; Wind is a huge opportunity in China but only works Offshore in Europe; Europe can't run cross-continent UHV grid systems like China due to beaurocratic impossibility; etc. etc.

That's an alternative for the seasonal storage problem, and currently the cheapest one. That doesn't mean other alternatives don't exist, just that those alternatives are not currently competitive with fossil fuels.

One should not use this situation that those alternatives can't exist or be reasonably expected to exist, or that a system using them would be more expensive than a system using nuclear. If that were a valid argument, one could equally argue that because new nuclear cannot compete with natural gas combined cycle for baseload, new nuclear is not an option.