Let's assume I hike in a region with a lot of streams, rivers and lakes (South-Germany etc.) not longer than for two days. Am I supposed to use a life-straw as my primary water-source or should it be considered just as an emergency tool?
Generally speaking, no.
Arguably you should never go for out for any kind of extended exhausting activity without ensuring proper hydration, i.e. packing enough fluids at least for your immediate needs.
The life straw will allow you to purify water sources you find up to a certain degree, but some concerns remain:
Lets say you planned well all your hikes and you know you will have constant availability of water all along the route then you could rely only on the Lifestraw. That said even for the best planned hike you can find that a seasonal source is not available in that particular moment or that some sources you counted on might have been contaminated by chemicals and end with a long stretch without any water... So particular attention will have to be put in planning and researching. If you plan on sleeping in a refuge then those will have water, if its just one of the rest huts or bivuac then some might have water closeby but not all do. Local clubs can be a great source of info but you will still remain uncertain.
There is the Lifestraw Go (like other similar products on the market) that is basically a lifestraw integrated in a water bottle, that might give you a bit more freedom, it holds a bit more than half liter. Given how you use the regular one, you might want to still carry a bottle because you might not be able to suck directly from the river or lake, so you collect with that and stick the straw in it.
Honestly I don't see the pros of not carrying absolutely any water outweighing the cons and I would consider sensible to carry 1 liter of water with me, clean or dirty. You can use a rigid bottle, its useful for other stuff too, or can rig a flexible bottle or bladder with the Lifestraw so to make a sort of inline filter, refill at regular intervals so to always have water and if its just for one or two nights not carry meals that require a lot of water for preparation and dishes washed.
I agree with fgysin's answer (no - water is very important - even with that equipment, you still need to find water, avoid chemical pollution, and access larger quantities of water for camp chores). I also want to add:
Redundancy. "Two is one and one is none" sounds silly until something breaks or is lost, and then you realize where that phrase comes from. If you only have one means of water purification and something goes wrong with it, you'll be very thirsty or drinking straight out of streams or bush-crafting some sort of container/filter (which isn't practical for a weekend hike, but you do need water on a weekend hike).
Versatility: An easy way to secure redundancy while also covering more necessary bases at once. You ask if a filtration device can replace water you'd normally carry, assuming there will be water 'stored' in nature and available for you to filter & enjoy. Having water storage is highly practical if not outright necessary. A canteen with a steel cup provides 2 water storage options, and at least one water purification option (boiling in steel cup).
Staying hydrated has a cascade of positive effects, and the opposite is true too (dehydration leads downhill fast). Having that convenient filtration device is good, but you shouldn't risk hydration by relying solely on that.
See for yourself: I recommend taking the lifestraw while also bringing a canteen you could fill, and try using the lifestraw as your primary/only water device to see how it works for you. It's worth challenging yourself as a learning experience - just be careful as water is key!