You are mixing up two different things. Aliasing is a problem caused by improperly filtering source material (either analog, or between digital stages after non-linear processing, such as the amp simulation discussed in your previous post which Robin linked to) in which material higher in frequency than half the sampling rate is present but not filtered, and so the sample values are reconstructed as signal below half the sampling rate.
That is primarily an issue with lower sample rates, not higher sample rates.
Your question about problems when using higher sample rates leads me to think what you are actually referring to is intermodulation distortion in the analog equipment, which is where high frequency signals interact with non-linearity in the electronics in such a way that produces lower frequency signals not present in the original.
There are two solutions to that: use equipment which maintains low distortion to very high frequencies, or use equipment which properly filters the input to reduce signal levels at frequencies that the equipment is not designed to handle. I guess a third solution, or maybe a subset of the second solution, is to provide filtering yourself in front of equipment which cannot handle high frequencies without distortion. That could be analog filtering, or you could just put a low pass filter on the master bus output if you insist on working at high sample rates with material that has a lot of high frequency content.