Everyone says it's not relevant and I don't think so.
And your right so. Failover of mongos instances is very important, without proper architecture to deal with this you could have a serious failure in your app. It also breaks the high availability of MongoDB.
What happens if the query router dies?
This is where you should really be putting in a seed list into the connection string in your driver, in this case the driver will do something along the lines of what it does with replicas and try and connect to other members on the list to resume as normal.
Is there an intended way for automatic failover to a second query router?
Provided you supply more mongos instance IPs to your applications configuration this should be pretty automated.
Or for load balancing between 2 query routers?
You can go that route as well if you want a only supply a single IP, but then you have to worry about that load balancer, and so on, and so forth...