The synthesis of product design concepts stands at the crux of early-phase development processes for technical products, traditionally posing an intricate interdisciplinary challenge. The application of deep learning methods, particularly Deep Generative Models (DGMs), holds the promise of automating and streamlining manual iterations and therefore introducing heightened levels of innovation and efficiency. However, DGMs have yet to be widely adopted into the synthesis of product design concepts. This paper aims to explore the reasons behind this limited application and derive the requirements for successful integration of these technologies. We systematically analyze DGM-families (VAE, GAN, Diffusion, Transformer, Radiance Field), assessing their strengths, weaknesses, and general applicability for product design conception. Our objective is to provide insights that simplify the decision-making process for engineers, helping them determine which method might be most effective for their specific challenges. Recognizing the rapid evolution of this field, we hope that our analysis contributes to a fundamental understanding and guides practitioners towards the most promising approaches. This work seeks not only to illuminate current challenges but also to propose potential solutions, thereby offering a clear roadmap for leveraging DGMs in the realm of product design conception.