The applications and services envisioned for the sixth Generation (6G) Internet of Things (IoT) communication systems will place different requirements on the system design. The current 5G waveform, Orthogonal Frequency Division Multiplexing (OFDM), suffers from a list of drawbacks that questions its suitability and ability to fulfill these prerequisites. Filtered multi-carrier waveforms provide viable alternatives for future mobile networks. Based on the best recent advances including contributions by the authors, this work provides a comprehensive assessment of the current status and future challenges related to the design of a next-generation Filter Bank Multi-Carrier/Offset Quadrature Amplitude Modulation (FBMC/OQAM) transceiver. We start by showing how the next-generation FBMC/OQAM waveform can overcome the drawbacks of OFDM. Furthermore, we highlight the advantages and possibilities of extending the next-generation FBMC/OQAM waveform for massive Multiple-Input-Multiple-Output (mMIMO) in well-identified 6G-IoT scenarios. Results show that the next-generation FBMC/OQAM receivers associated with short prototype filters can unleash appealing properties for 6G-IoT applications. Considered a cornerstone for grant-free spectrum and massive access, asynchronous communications are shown to be achievable. Furthermore, a largely improved robustness is observed compared to OFDM under different channel impairments such as carrier frequency offsets, timing offsets, and multipath channels. Compared to the original FBMC/OQAM associated with long filters, this next-generation transceiver achieves a reduction in complexity down to a comparable level to OFDM. Finally, open research opportunities and challenges for the next-generation FBMC/OQAM waveform are discussed.