Is it easily possible to merge these two points into one point which has two bezier-handles: the left from the former left point and the right from the former right point?
No. Not with the stock version of Illustrator.
Because any alteration to either anchor's position will ultimate alter the path, there's no way for Illustrator to calculate the removal of one anchor and retain the path position. Illustrator, out of the box, is simply not that smart.
A few unworkable methods:
Object > Path > Average can position both anchors into the same location. However, since the anchor's move, the path is altered.
- One could manually move one anchor on top of the other. But, again, moving either anchor alters the path.
In both these cases, after the anchors are on top one another, you could remove one of them. But still, removing one anchor removes it's Bezier handles as well, thus even further altering the path.
The only method I know is to use the Smart Removal feature which exists in http://www.astutegraphics.com VectorScribe plug in. The smart removal feature will allow you to select and remove one anchor and the path position will remain in place, altering the Bezier handles of the remaining anchor to match the path rather than altering the path to coincide with remaining handles.
Some slight alteration may still occur. However, the smart removal features is the only thing I'm aware of which is even remotely capable of doing what you are asking.