Your point about presets is one of the main things that pushed me into the modeling realm. I was running analog pedals into a tube head and cab, but it lacked body unless I turned the volume turned up to about about 3/10 on the control (107-110 dB in the room). That was bad for my hearing (ringing in my ears after playing more than a few minutes) and my wife wanted none of it, so I only got to play that way when she was not home. It was awesome and I still do that on occasion, but I wanted to be able to play guitar more frequently than that and in a way that wasn't going to kill what is left of my hearing.
I bought a load box and IR loader with headphone out to try and solve the need for lower volume. It became apparent that the settings I used with the cab didn't inspire me when playing though headphones. Every time I wanted to switch from the headphone setup to the cabinet setup I had to re-cable things and spend the first few minutes getting the amp dialed in again. It was a major inspiration killer and I would go weeks without switching back and forth because it didn't feel worth the effort for one evening of playing.
The thought that I could make individual presets configured for a specific guitar through a specific cabinet or speaker system and recall them in seconds was very appealing. Digital modeling makes it easy to switch rigs and that is one of the reasons I play my digital gear way more than my analog gear. There is almost no time penalty for deciding that I want to play with another pallet of sounds or to use a different monitoring rig. I have everything routed so can use over the ear headphones, IEMs, studio monitors, ""FRFR"" speakers, or a pair of 4x12 cabinets in stereo and all it takes to swap between them is a few button presses and flipping on the power switches.
If I want a real amp, I just swap my cable to the proper amp input, power it on, and go. I could do even more with the analog gear integration since I have load boxes, tube power amps, and analog pedals, but I just haven't found the desire to make it happen.
We are in the golden age of gear.