Before revision:  Moreover, we outline that both problems remain NP-hard even if the input is planar. On the positive side, we give a polynomial-size integer linear program and show fixed-parameter tractability in the number of shared bend points.
After revision:  This inapproximability even applies to instances with only \ell=2 polylines. However, we identify the sensitivity of the solution to the choice of \delta as a reason for this strong inapproximability. In particular, we prove that if we allow \delta to be exceeded by a factor of 2 in our solution, we can find a simplified polyline bundle with no more than O(\log (\ell + n)) \cdot OPT bend points in polytime, providing us with an efficient bi-criteria approximation. As a further result, we show fixed-parameter tractability in the number of shared bend points.