In Germany it's not the job of a prosecutor to get the maximum possible sentence, so no the problem doesn't exist in the same way in Germany. If someone in Germany commits a crime that gets 3 years and another that's 4 years that doesn't simply add up to 7 years. Our system is much more well designed.
Being tough on crime happens to be a politicized topic in the US and there are many people who do hold the opinion that the US incarnates a percentage of it's population that's significantly to high. It's no Republican vs. Democratic issues but that doesn't mean it's not political in nature.
In this case I'm not sure whether blackmail is really the right term. Wikipedia defines blackmail as "Blackmail is an act, often a crime, involving unjustified threats to make a gain or cause loss to another unless a demand is met." Is using a valid law for charge inflation an unjustified thread? That depends a lot on your political beliefs.
The heuristic that one should always resist blackmail seems a good one (no matter how tricky blackmail is to define). And one should be public about this, too; then, one is very unlikely to be blackmailed. Even if one speaks like an emperor.
But there's a subtlety: what if the blackmail is being used against a whole group, not just against one person? The US justice system is often seen to function like this: prosecutors pile on ridiculous numbers charges, threatening uncounted millennia in jail, in order to get the accused to settle for a lesser charge and avoid the expenses of a trial.
But for this to work, they need to occasionally find someone who rejects the offer, put them on trial, and slap them with a ridiculous sentence. Therefore by standing up to them (or proclaiming in advance that you will reject such offers), you are not actually making yourself immune to their threats. Your setting yourself up to be the sacrificial one made an example of.
Of course, if everyone were a UDT agent, the correct decision would be for everyone to reject the threat. That would ensure that the threats are never made in the first place. But - and apologies if this shocks you - not everyone in the world is a perfect UDT agent. So the threats will get made, and those resisting them will get slammed to the maximum.
Of course, if everyone could read everyone's mind and was perfectly rational, then they would realise that making examples of UDT agents wouldn't affect the behaviour of non-UDT agents. In that case, UDT agents should resist the threats, and the perfectly rational prosecutor wouldn't bother threatening UDT agents. However - and sorry to shock your views of reality three times in one post - not everyone is perfectly rational. And not everyone can read everyone's minds.
So even a perfect UDT agent must, it seems, sometimes succumb to blackmail.