Is there a single word for doing something despite the fact that it might cause problems later?

Solution 1:

Impetuousness:(Cambridge Dictionary)

the quality or fact of doing things suddenly, without considering the results of your actions:

I think this word is closely related to your idea, though not an exact word. If an idiomatic phrase is acceptable, the below one is suitable.

dig one's own grave (The Free Dictionary)

Fig. to be responsible for one's own downfall or ruin.

If you try to cheat the bank, you will be digging your own grave.

Those politicians have dug their own grave with their new tax bill. They won't be reelected.

Solution 2:

How about shortsighted?

[Merriam-Webster]

1 : lacking foresight

shortsighted politicians who only care about how they do in the next election

A perhaps more critical version of shortsighted is myopic:

[Merriam-Webster]

2 : lacking in foresight or discernment : narrow in perspective and without concern for broader implications

But only a myopic angler would fail to recognize the alarming signals in those unusual conditions. —Pete Bodo

However, these are both for people who only think about the short term, not caring what happens in the future. They may be aware that it will have detrimental long term effects—or they may not be

If you're talking about people who do know it's bad in the long term, but don't care anyway, that's more commonly known as instant gratification (or immediate gratification).

This comes from Freud's idea of the pleasure principle.

In her article "What Is the Pleasure Principle? How the Pleasure Principle Helps Motivate Behavior," Kendra Cherry says:

In Freud's psychoanalytic theory of personality, the pleasure principle is the driving force of the id that seeks immediate gratification of all needs, wants, and urges.

This is in contrast to delayed gratification, where something may be of more benefit if effort is put into it in the short term, or if you simply wait.

Appropriately enough, given your assertion that single words are easier to come by in German, the single German word for pleasure principle is Lustprinzip (Collins).