The problem occurs with amps and pedals as well as sims.
If you use a lot of gain/compression that boosts the noise coming from the guitar itself and any pedals before the gain is added.
Gates are a last resort fix that’s rarely satisfactory, and they always affect both the attack and sustain of the guitar.
Humbucker-equipped quitars shouldn’t be as noisy as single coils, but even a well shielded guitar with good humbuckers will still pick up some electrical buzz from sourounding stuff. Guitar leads also pick up noise and can act as ariels, especially with some pedals such as simple fuzz circuits. Computers put out a lot of electrical noise as radio which guitars pick up and send to the amp. Changing the angle between guitar and computer/monitor can sometimes make for a big decrease (or increase) in the noise picked up by the pickups.
Paying attention to gain staging can go a long way towards minimising noise. E.g. running a distortion pedal that boosts the signal a lot and creates noise itself into another similar pedal, compressor or a high-gain amp is a recipe for a lot of noise. For minimal noise, pedals that generate noise are best used into cleaner amps that boost the noise floor less than a high gain amp channel. The ideal is to get the noise floor as low as possible by better gain staging and then consider gating as a last resort. A gate that only affects certain frequency bands, such as a couple of Bozdigital’s, can be useful on guitar and be much less obtrusive than a full-frequency gate.
It does have to be said that some amp sims are very noisy themselves, maybe even noisier than the amp they are trying to emulate. Same with some effects emulations, which start with over the top settings and noise levels. The Amplitube Big Muff being an example of one.