What you're writing isn't really correct either, this partly stems from the difficulty of what we mean by "robust". To increase throughput (i.e. bitrate ) we c

What you're writing isn't really correct either, this partly stems from the difficulty of what we mean by "robust". To increase throughput (i.e. bitrate ) we can either increase the channel bandwidth or the SNR (and use that SNR for higher modulation formats). Increasing the channel bandwidth does increase the noise power (assuming matched filtering) but we typically also assume that the psd of the signal stays the same => signal power increases and SNR stays the same. If we mean by "robust" that the signal is not as susceptible to fluctuations of the noise, than increasing the bandwidth could help. Assuming we want the same bitrate, we could use the larger bandwidth to reduce the modulation format and thus the required SNR while keeping the bitrate the same. However a larger bandwidth typically also increases probabilities of impairments (interferers, filtering...) but this is typically still a win, because capacity throughput is linearly proportional to bandwidth but only logarithmically to SNR.