Anything is technically possible. However, there are a vast array of scenarios that make it extremely difficult and not really worth the time to setup.
You can easily use the current bots and profiles to do all of the leveling (communities are faster though), getting gems, gold, basic gear, crafting materials, rifts, GRifts, bounties, keywardens etc.
Then you can manually upgrade your artisans, equip follower, to the crafting requirements, get the cube, etc. Manually upgrade your gear as you unlock haedrigs gifts. Set torment higher as you can to complete tasks.
Auto-Equip is just not setup for advanced gearing with set bonuses, setting the proper skills, re-rolling items, equipping gems, etc. Even if it could, it would have to be able to determine what torment level based on so many different factors that it would border on artificial intelligence.
This would require a lot of large advanced in the bot logic for limited payoff. Outside of the set dungeons, it only costs me an hour or two each season between changing gear and profiles to get the journey complete.
The main thing that most people bemoan is set dungeons. Realistically, I could see where it would be possible for the bot to run the dungeons... However, A specific build combat routine would have to be coded for every single set dungeon that would only be used for that one set dungeon. That's a lot of work for limited payoff. You're talking 20+ routines just for the dungeons which is more than we currently use in general.
...And they would have to be very advanced and extremely fine tuned to do the specific tasks for each dungeon. Those builds would require specific gear and skills to be set for it to use the build properly (which you would have to do manually and could take a lot of time).
Then a specific profile would have to be written in tandem with each set to properly handle the map along with the gear/playstyle.
Once all of those thousands of lines of code are written, it will have to be massively tested and fine tuned.
And at the end of all that, it's still a crap shoot because of the method the bot uses to explore the map nodes leading to wasted time.
TL : DR I am not a developer here so I don't know the true boundaries, but... The bot would need to have exploration method redone and there still wouldn't be any promises on the clear speed (mob settings for tasks vs. clearing all enemies, backtracking to find enemies quickly, etc). You would still have to manually do gearing, and if the builds would need to be very specific to get the best performance, you will have to spend a lot of time getting geared right. There are too many variables that would be impossible to account for with gearing to do it automatically. Each class has 3-5 builds coded in now and would need that number nearly doubled, each build would be more advanced that current ones since they need specific logic for specific tasks. Profiles would need to be made for each map. All of that massive amount of work for a build that will be used for one set dungeon and not touched again.
I just really happening since doing all the set dungeons gets you almost nothing, and to get seasonal achievement only requires 1 mastery.