Are there other uses for the value of RMS current besides heating computations?
RMS is nearly always associated with power, but there are many times you want to know power that don't involve heating resistors. For example:


The power sent to a speaker becomes sound waves. The RMS value of the waveform corresponds to the perceived loudness of the sound.
Signal-to-noise ratios are power ratios. Therefore, you want to compute the RMS values of the signal waveform and the noise to get a SNR value.
In electrical power transmission, it's the RMS values of voltage and current that correspond to the power delivered to, say, a motor (assuming the power factor is near unity, of course).


There are many more examples. The point is, in most forms of AC signal analysis, the RMS value is nearly always the more useful value &mdash; although there are times when you need to be aware of the peak value as well.