We study the performance scaling laws for electrical-domain combining in photodetector (PD) array-based receivers employing intensity modulation and direct detection, taking into account the inherent square-law relationship between the optical and electrical received powers. The performance of PD array-based systems is compared, in terms of signal-to-noise ratio (SNR) and achievable rate, to that of a reference receiver employing a single PD. Analytical and numerical results show that PD arrays provide performance gains for sufficiently narrow beams and above an SNR threshold. Furthermore, increasing the number of PDs alone does not enhance performance, and joint optimization of beam pattern, transverse electromagnetic mode, received power, and PD positions is necessary. Our model and derived insights provide practical guidelines and highlight the trade-offs for the design of next-generation high-bandwidth PD array receivers.