The idea that this technology is "the most popular" is incorrect as is the idea that tube amps are unreliable.
The katana and fender GT sound "fine" but the assertion that they can model traditional tube amps well enough for stage use is also a little suspect. Those specific amps sound thin and lifeless compared to the amps they attempt to model.
Where these types of amps shine is that they're lighter and you can have a more consistent sound at lower volumes. For a person in their house who isn't really worried about having a specific sound or may not even know the difference between british and american voiced amps these are great options. Also the volume issue only comes into play when we're thinking about gain and compression. My fender Deluxe Reverb sounds amazing at low volume.
The AxeFx and helix stuff is a little better but that stuff is way more expensive than your average tube amp, particularly on the used market. Your average 40 watt tube amp from fender, vox, marshall, etc will run you $700-$1500 while these high end modellers can easily be $2500+.
As far as tube amps being unreliable goes I'd love to see some sources on that. I've played fender amps from the 50s and marshalls from the 60s that sound every bit as good today as they did when they were made.
I work in very high end music retail where I'm fortunate enough to get to play all kinds of new and very old gear. I can confidently say that modelling is getting better and has drastically improved in the last 20 years but still has a ways to go if it's going to completely replace tube amps for stage and studio use.