Enzyme-responsive polymers and their assemblies offer great potential to serve as key materials for the design of drug delivery systems and other biomedical applications. However, the utilization of enzymes to trigger the disassembly of polymeric amphiphiles, such as micelles, also suffers from the limited accessibility of the enzyme to moieties that are hidden inside the assembled structures. In this Perspective, we will discuss examples for the utilization of high molecular precision that dendritic structures offer to study the enzymatic degradation of polymeric amphiphiles with high resolution. Up to date, several different amphiphilic systems based on dendritic blocks have all shown that small changes in the hydrophobicity and amphiphilicity strongly affected the degree and rate of enzymatic degradation. The ability to observe the huge effects due to relatively small variations in the molecular structure of polymers can explain the limited enzymatic degradation that is often observed for many reported polymeric assemblies. The observed trends imply that the enzymes cannot reach the hydrophobic core of the micelles, and instead, they gain access to the amphiphiles by the unimer- micelle equilibrium, making the unimer exchange rate a key parameter in tuning the enzymatic degradation rate. Several approaches that are aimed at overcoming the stability-responsiveness challenge are discussed as they open the way to the design of stable and yet enzymatically responsive polymeric nanocarriers.