bluice, you're repeating a lot of arguments that get frequently made, and frequently rebutted.
The UK has 4 GW of interconnectors and another 8 GW under construction or planning:
https://www.ofgem.gov.uk/electricity/transmission-networks/electricity-interconnectors Demand rarely rises above 40 GW and is on a downward trend, although EVs may reverse this. 12 GW is 30% of 40GW, so 30% of a worst-case scenario is covered through interconnectors. This only includes interconnectors planned at the moment, and due for completion by 2022, so it could obviously go much higher than this in the long term.
Demand side response (DSR) can provide a significant amount of spare capacity for short-term spikes in demand and/or drops in renewable generation. Lots of power companies are investing heavily in this, so that even relatively small-scale users can take part in this market. EVs and vehicle-to-grid technology will potentially play an important role here.
Grid-scale batteries do exist, and are increasingly being deployed. Not on a huge scale yet, but growing. Li batteries is the main technology at the moment, but lots of other technologies are being tested and deployed on a small scale.
In addition, you have existing hydro (including pump-back and pumped storage), which can be turned on and off in response to changes in demand, nuclear and, as has been said a few times already on this thread (if my memory serves me right), existing natural gas-fired power stations that can step in to cover short-term requirements.
Finally, using arguments about why renewables will never cover 100% of demand when most countries are in the 10-30% range is also a bit of a straw man. It will take us decades at current rates to get to 80% let alone 100%. Let's speed up deployment and get to 60%+ as quickly as possible. That's when things start getting a bit trickier, but technology will almost certainly have caught up by then.