It is a very solvable problem, and mechanical or thermal batteries are likely to be at least part of the solution. Of the three kinds of gaps/shortfalls that grid storage would have to cover, the milliseconds-long and hours-long gaps are probably the easiest to solve. The days-long gaps (stretches of cloudy days, low winds for extended periods) is probably the most expensive to solve, but even those are not really that difficult (hydro storage is a tested technology that works well and HVDC transmission linking regions together can allow local shortfalls to be covered by remote surpluses). It’s all more a matter of building capacity than needing new technology to solve an unsolvable problem, from what I understand

Longevity is the big problem. Every practical method of energy storage I can think of is negatively impacted by frequent charge discharge cycles. Even a flywheel like you suggest would eventually need new bearings, need rebalancing, etc…