You mentioned 12K and above, but realistically that number could depend on your audio output source. Depending on your speakers or headphones, the high cut can vary. For me, the high cut can help to simulate the fact that we don't hear our amps with our ears at speaker level. We are usually off to the side and above. It can also depend on the amp.
Also, don't hesitate to bring the low cut up passed 80 when you are playing in context with other recorded music, tracking/mixing, or in a band mix. I've been experimenting a lot with recorded tones and comparing what my ears perceive as a good low end vs what is on recordings I love. For example, I've noticed that Malcolm Young's rhythm tracks on a lot of AC/DC stuff seem to have a low cut at around 120-140. Suprising to me. Looks like the Black Crowes Amorica is somewhere in the neighbourhood of 100-120. The magic 80 that I see so often on message forums and dialed in on presets for amp modellers is perhaps best suited for live use not recording. You'll get too much low end build with drums and bass in a recorded mix without a doubt.
Also, don't neglect the impact that an EQ can have going into an amp (see Brian May's boosted midrange god-like tone). Amplitube 4 uses a dynamic amp modelling system and amps react like they do in the real world. Shifting EQ before the amp can do a lot more to the quality of the harmonic content than it would coming after. It will not only do things like reduce or add bass, middle, and treble, it will change the character of the distortion and harmonic content. Can make a Fender sound like Vox etc. in some cases.
People seem to be very impressed with the Strymon Iridium and for the 3 or 4 days I've been testing one, it does seem to have some nice tones. However, I was shocked to hear that the stock IRs look to have a low-cut/hi-pass somewhere in the neighbourhood of 140. I understand their choice, since this works so well in a mix (live and recorded), but I do think it's an odd choice to make since so many buyers would be picking up an Iridium for practice/solo playing at home. Not having that 80-140 can be less than satisfying when playing on your own and is downright
when you A/B something like Amplitube and the Iridium. Amplitube sounds like a SuperHiFiUltraHD3D billion dollar amp simulator with the amp in a real room and the Iridium sounds like an overdrive pedal through a 30 band EQ and a compressor/limiter going direct to the board when comparing. So much of that perception comes down to EQ. I prefer companies to leave it to user to find the cut-off points at the top and bottom of their guitar, depending on what is needed and appropriate for a given context. Changing up IRs makes all the difference for the Iridium because of the expanded range of EQ. Again, just an interesting choice by Strymon for stock cabs.
Eq is a rabbit hole that can make or break your experience with modellers like Amplitube etc. Be patient and find what works for you and the context of your playing. Amplitube has all that is needed to get a tone that is equal to or even better than the 2000$ big boys on the market. I'm just waiting for hardware product that has built in DSP and Amplitube. Come on IK!!!!