Hello Ulysse,
There are a few different ways that you can increase the power reserve.
You can decrease the power demands by reducing the size of the balance, decreasing the beat rate or increasing the efficiency of the escapement. Then you change the gear ratios so that the (now) excess power of the mainspring will be released more gradually. Most extended power reserve movements these days have smaller balance wheels and some of the modern, high-tech escapements are more efficient. These possibilities don't in-and-of themselves introduce more stress in the power train.
You can use a stronger mainspring and simply add an extra wheel to the gear train. This is the way 8-day alarm clock movements worked primarily and yes, this does introduce a lot more stress on the barrel and the first wheel in the power train.
You can use a longer mainspring, which will give more turns of the barrel but needn't be particularly stronger.
Or you can use multiple barrels, which also doesn't necessarily mean more stress in the power train. Barrels working in series will have the same general effect as using a longer (not stronger) mainspring, and barrels working in parallel will have some amount of balancing effect on the wheel they drive which may mitigate some of the additional stress.
Every solution is a trade off and there are no absolute or truly optimized answers, just different engineering choices and priorities, and these can change with the demands of the consumer market, advances in the mechanical solutions available and advances in materials.
_john