Confusion in Peak to Average Power Ratio (PAPR)
Preference for low PAPR is subjective. From a power efficiency and unit cost perspective, low PAPR is certainly beneficial, but from a spectral efficiency perspective, it typically isn't. High entropy modulation means high PAPR (i.e. signal looks more like Gaussian random process).

A low PAPR can mean that less backoff is needed in a power amplifier, and hence better power efficiency can be achieved. Similarly, low PAPR means less headroom required in an ADC and thus allows for lower-precision in the ADC. These back-off/headroom requirements for TX and RX are closely related to PAPR. Some typical systems considerations that are linked to system requirements:


modulation - higher-order QAM and/or multicarrier modulation means higher PAPR, which means an increased budget for headroom across signal paths.
fading - not normally a part of PAPR, backoff for fading is closely related and arguably becomes an overall PAPR consideration for RX paths (we normally reference PAPR as signal-related, but fading typically increases the ratio)
code rate and blocksize - high coderate and large blocksize, particularly at high-order modulation, means that the signal can be highly susceptible to clipping, non-linearity, and other impairments, and thus we need to allow headroom for the rarest of peaks (definition of PAPR is somewhat subjective, too; are we worried about the 1E-3 probability peak or the 1E-6 probability peak?)
bitwidth - ADC, DAC, and processing chain bitwidth. Higher PAPR plays here, too. For higher PAPR, more backoff from full scale is needed to avoid distortion of the peaks. This requires more bits and analog linearity for signal representation and processing.


For multicarrier modulation (OFDM, DMT, etc), PAPR can certainly be problematic. To visualize, try modulating a high-order QAM constellation on subcarriers using an FFT (IFFT). The sum of tones results in a constructive and destructive combining across the IFFT symbol, giving high PAPR.