Since I do this for a living I'll chime in. The room is 1st, equipment can't change physics. Take the best equipment in the world and put it in a racquetball court and it will still sound terrible. EQ, DACs, AMPs, Processors, etc. can't change how sound is going to bounce around the room. This isn't to say the other stuff isn't important, it is. But, as long as you have decent quality gear the room will be the biggest influence in the sound.
You are incorrect about studio monitors and off axis response. Most of the better studio monitors have excellent off axis response. Genelec 8260s being the best speaker I've measured either pro, audiophile, or HT. Harman, Genelec and others have done some excellent research on speakers and off axis response and how it relates to quality of sound perception. The pro world I feel has led the way in this area. However many of these companies are players in both markets.
Active speakers have a lot of advantages over passive ones and there is nothing wrong with using them in the HT environment. The disadvantage to active speakers is wiring. You have to get a signal wire and power to each speaker.
From research we know that the people prefer speakers that have a flat frequency response both on and off axis. Depending on the off axis response of a speaker will help determine where that speaker and acoustic treatments are best placed within a room.
As far as studio vs. HT there are some room differences typically. Many studios are more 'dead' than typical HT. Studies have shown that people prefer a slightly more lively but not overly reverberant room. Even recording engineers studied have preferred listening to a room with more reverberation when listening for pleasure. However, prefer a more 'dead' room for trying to pick up details of the material while working.
These are big generalizations though. There are over 100,000 recording studios worldwide and they vary greatly in their set ups and room acoustics. This is one reason with music it is often difficult to hear exactly what the artist intended as we don't know the environment it was mixed and there is no standard for recording studios.
By contrast there is a standard for movies and most movies the final mix is done in a dubbing stage. A dubbing stage is a theater with a mixing console in the middle of it, it is NOT in a small space like a recording studio. This is where the final mix of a movie is put together. There are only about 20 dubbing stages worldwide which most of the big movies final mix are created. These are very similar acoustically as they follow standards. If you can create your HT to replicate the acoustics of these dubbing stages, you will hear it how the material as intended.
Processors in the recording environment are huge. However, it is not processing like we think of it in the home. At home we think EQ like Audyssey and maybe some DSP programs like Pro-logic. Processing in the pro world is about altering the recording with reverb, exciters, compressors, limiters, EQ, other effects, etc. Although room EQ may play a role it is not what I think of when someone talks about processing in a studio. Cheaping out on these components will not make the best recordings and there is a lot of keeping up with the latest and greatest in the processing arena.