Real race car drivers sometimes heel-toe, watch austrailian V8 supercars on youtube, they have alot of foot cam videos of it. About 4 out of 5 will show heel-toe footwork. And just about every other race car foot cam video on youtube will as well. I looked at alot of these videos when I was learning the footwork.
However, V8 supercars also have ignition cut for upshifting, its done with a microswitch on the shifter that allows the driver to cut ignition while he changes gears with the H-pattern shifter. So they generaly don't have to lift while changing up. Some drivers don't use the clutch at all and brake with thier left foot, but I have only seen this in a video once.
In a sequential box there isn't a neutral state between gears, it just switches to the next as it dissengages the last. Heel-toe on a sequential requires you to have the clutch in while you blip, if you do. And there is no way to double clutch on a sequential.
Old F1 in the 60's had H-pattern gearboxes and they also used heel-toe back then.
As far as rev-matching and lifting off on a sequential.
Generaly, if the car doesn't do it for you, it's ok to do it for the car. I prefer doing it myself because it gives me the control of when and if I do it. Sometimes it can be useful to not rev-match, and if you know the car well enough you don't need to use the clutch all the time.
It's all about knowing the car and what you need to do and when. I don't rev match in the FBM, because it isn't critical to do so, and in the BF1 most of the time you realy dont have time unless you have a bionic foot. But in the XRR it can help keep the car balanced if you are running lower downforce settings.