I'd say it's critical in the UK: a combination with popular TV programmes and the UK's citizens being likely to own an electric kettle: https://youtu.be/WCAzalhldg8
Millions of people turning on water heaters within a few minutes will have an impact on any electric supply.
Oh, very much so! Ad break during popular soap operas and a lot of kettles go on simultaneously around the country. It's very well known to electricity suppliers.
So, when a TV studio broadcasts, the electricity for everyone to watch it is paid for by the viewers. The studio only pays for the power to either broadcast from the TV antenna, or the power to send the signal to the cable company.
But when you watch a broadcast on the internet, not only are the viewers paying for it (their internet), but also the company is paying for the internet on their end (all clients connecting at once, using all that bandwidth), as well as all the servers to handle all those connections.
If TV broadcasts worked the way the internet did, a broadcasting company would have to be able to handle the incoming power load of every household's power bill combined, simultaneously.
It seems like the internet is poorly architected! The company should be able to send its one broadcast stream out, and it should be distributed to all the client machines, without the broadcast company needing to directly connect to (and duplicate) the signal across every client themselves.
In the early internet, where every device has a public IP and the only firewall is the one you should've set up, multicast penetrated through all networks and a single packet stream could be subscribed to from anywhere, replicated across the internet.
These days, only IPv6 capable networks (so half of the web or so) satisfy the necessary requirements for such a system and internet multicast has wisely been turned off for the enormous DDoS/bandwidth waste it implies.
This mechanism is still used on some TV networks, though, especially digital ones that come over fiber. There is a single stream of packets generated to send to all subscribers that the subscriber devices can then subscribe to with the proper network config. This is often accomplished through IGMP and other such multicast protocols.
As for sending a single broadcast stream out, that's exactly what online streaming services do. A 30mbps Twitch stream with a million viewers doesn't require you to get a data center's worth of internet capacity at home; instead, you upload a single stream to your favourite service and that service replicates the stream for you. You can set up such a system yourself if you want to stream from home, have a cloud server with good internet, but only cable or DSL upload speeds through somerhing as simple as nginx with RTMP enabled.
Possibly, who knows! On the one hand you lose a clear predictor of sudden power peaks, but on the other hand the ability to pause/resume/pick your own time probably spreads out the usage more across the day so the kettles have less of a direct impact.
I wonder if these days the grid operators also monitor internet statistics in some way.
This might be more applicable in 120V America, but it would be nice to have a kettle that charges a battery for a quicker boil when it needs to be used. Given that, it might not really matter if everyone used their kettles at once, since they would just recharge slowly afterwards.