Modulation with Maximum Likelihood decoder and capacity
You are correct that OFDM has several drawbacks, such as the required guard band, number of pilots, and its high PAPR. Many alternatives have been developed, with different sets of pros and cons. Implementation simplicity remains OFDM's most important advantage.

One thing to keep in mind is that OFDM is designed for the wideband (frequency selective) fading channel. The capacity of such a channel is not the usual $C=B\log(1+SNR)$, which only applies in the AWGN channel. Since the fading channel is time-varying, other measures of capacity (such as outage probability) become more important.

To answer you specific question: to my knowledge, it is impossible to reach capacity without coding, except when $\text{SNR} \rightarrow \infty$.