I don't know about Germany, but in New Zealand we have a very similar way of voting in our members of Parliament so I will take a stab at why you would not want your president to be able to veto a law thing.
Unlike the US, we do not directly elect our head of state (I presume this is also true for Germany as well). Instead we vote for the party that we want to be in power, based on their policies and the party appoints a PM. This is actually quite common in many places, and it means that the Prime Minister can change inside a term. e.g. The United Kingdom had a PM change from Blair to Brown without an election. In the US if the president was to resign, the VP would become the president, it cannot be reassigned based on party politics. In practice the choice for PM is announced before the election, so many people do vote based on who they want their prime minister to be.
[The US is even stranger here, as you get the right to vote for your sentators, representatives and your electoral college member, but that is a whole different digression.]
The prime minister does have a fair amount of power, and does a bunch of figure head stuff (negotiate treaties, etc). But as it is not an elected position, the PM has fairly limited legislative power. The idea of one person vetoing a law that the other democratically elected MPs voted for would not be accepted, the PM already has a fair amount of unofficial power in the form of increased media time, and influence over the majority collation at the time. The fact that Germany has a system where the PM can overrule a law that violates the constitution is, in my opinion, a good thing.
[The closest NZ has to this is the governer general -- as a member of the commonwealth our official head of state is the Queen of the Commonwealth. She appoints the GG who then approves laws in her place. The GG could, in principle, turn down any law for any reason but that would quickly turn public opinion against being part of the commonwealth and would probably make NZ reconsider its position within the commonwealth.]
In contrast, ignoring the issue of the congressional college, the US populace votes directly for the position of president on the understanding that this one position will have a lot of legislative power in the form of vetos. Whether that is too much of a concentration of power for a single individual is up to you to decide, but at least it is an elected position. Ignoring our governor general (who theoretically has a lot of power, but would lose it is she ever tried to yield it) our system does not have as much power with a single person, and our elections for (psuedo-)head of state tend to be much more civil that the USA counterparts.
Hope this helped explain the origins / reasons for the differences!