For the past year in the UK the average is ~30% generation from wind. https://grid.iamkate.com/
So seems it's possible. Swings in generation are dealt with via inter-country interconnects, pumped storage and gas turbine generation. Nuclear adds a steady base.
The UK's prices are a political choice due to the mapping of voters over the energy generation distribution.
By breaking the country in to zones, where the electricity that's bought can actually reach the users they then apply the actual economics of the system properly, and encourage suppliers to build where the demand can be satisfied by them.
Situation is very similar in Germany - most industry is concentrated in the south while most productive wind in the north. In the past it didn't matter since prices were similar with coal. But now, since you can't magically create wind in low wind/unproductive areas, the options are either split zones and kill part of industry, which Germany doesn't want, or to keep a single zone and build expensive transmission like sudlink.