Semiconductor quantum dots (QDs) in the InAs/AlGaAs system are of great importance due to their promising optoelectronic and nanophotonic applications. However, control over emission wavelength governed by Al content in the matrix is still limited because of an influence of surface Al content on QD size and density. In this paper, we study the growth of In nanostructures by droplet epitaxy on various AlGaAs surfaces. We demonstrate that an increase in the Al content leads to a decrease in the droplet density and an increase in their size, which contradicts the Stranski-Krastanov QD growth. Using a hybrid analytical-Monte Carlo model, we explain this phenomenon by the fact that In adatoms acquire higher mobility on a first indium monolayer which is bound to surface Al atoms. This assumption is confirmed by the fact that a temperature decrease does not lead to a great increase in the critical thickness of droplet formation on the Al-containing surfaces whereas it changes considerably on the GaAs surface. Furthermore, the Al content influence on the formation of In droplets is much less significant than on the growth of InAs QDs by the Stranski-Krastanov mode. This gives an opportunity to use droplet epitaxy to control the matrix bandgap without considerable influence on the QD characteristics.