.. the current passing through the connectors and switch is more (creates heat) that the switch/connectors can handle. ...
I would agree with the switch being unable to handle it (on the pre-Roadsters anyway) but respectfully, not on the connectors - assuming the connectors have not been compromised*.
The Touring only has one headlight, so you're knocking 5 off vs the load on the early R3's. NOte that there are no examples (I could find) of Touring model key-switch failures.
*This one - and one other here on the site - have had issues with connector position 1 terminal (which is the supply current for headlight, starter solenoid and ignition circuit current) but I would have to believe this was due to a loose-fitting female terminal - a loose fit creates local heat and then it burns. This is not exactly a prevalent problem on Tourings - those Sumitomo connectors are excellent quality & if assembled correctly should definitely not fail.
Even something like sticking a test probe into the female is enough to compromise it. Not saying that is what happened here, but I honestly don't believe this is a widespread issue (like the early bike key-switch failure)
You could say - ah but the later ones have the Sumitomo connector and that is the new 'weak point' in the chain vs the early; however the early models changed to that connector in 2008 - and on those the weak point remained at the key-switch, not the connector.
But absolutely, if you reduce the load through that circuit, you certainly reduce the likelihood of failure, wherever it might want to occur.
One extremely easy/low cost way to reduce the load through that circuit (on a Touring) is to remove the green wire from the Fuel Pump relay and replace it with a fused wire from the battery.