All of these tickets are only for local/regional trains, not the faster/long-distance trains. You can get from one end of the country to another by changing trains a few time, but e.g. getting from Munich to Berlin would be 6h (direct) with fast trains and 10+ h (changing 3 times) with the regional ones.

The subscription model is intentional - this isn't meant to help tourists or to be bought when you need it, it's meant to make sure people have already pre-paid the cost when making a decision whether to take a train or a car (by being cheap enough that people subscribe even if they don't use it all the time).