After watching "Star Trek Beyond", I do agree perhaps more screen time and development for Krall would have improved his characterization. However, it does allow for some fan conjecture on his personality.

This is based on some fan theories and my own speculations:

Edison was possibly a sociopath when he started out as a MACO, and enjoyed fighting a bit too much, more like a Klingon than human. Some fan theories suggest that he may not have been on NX-01 during the Xindi Conflict, but was part of a mop up campaign of Xindi-Reptilians and some Xindi-Insectoids. During that time, MACO and Starfleet had interservice rivalry akin to many armed forces today. Heck, Major Hayes and Lt. Reed did beat the crap out of each other once in ENT: "Harbinger".

While he was certainly decorated for his actions, maybe even many fellow MACOs saw him as too battle-happy. (Think of Jack Churchill, the crazy British soldier with a claymore and bagpipes circa WWII). By the time of the Romulan War, he may have continued to be an efficient soldier, though not too concerned about the welfare of personnel who didn't agree with his views. Some of those awards he got could have been from sacrificing men, details that were glossed over since Starfleet and the MACOs needed heroes to rally around during that war. Think of WWI commanders who seemed to recklessly throw hundreds of lives away by ordering them into no-man's land.

All this does catch up to Edison when Starfleet and MACO are merged together. Starfleet is probably more stringent about the psychological profiles, though some still evade screening like the crazy commodores and other officers in TOS. They may have realized that Edison wasn't suited for a top of the line starship, and may have feared him going rogue with the latest Starfleet weapons.

Enter the Franklin, which I conjecture may have been an outgrowth of the NX Project. The bridge window at least for Franklin may have been a holdover from the cockpit windows of the NX-Alpha, NX-Beta, and NX-Delta prototypes. Her shape may have been further developed into the Akiraprise look of the NX-class. The Franklin was meant to be a small, long ranged surveyor, much like the Nova-class starships of the 24th century. For the technology of the time, Franklin probably is too small to accommodate photonic torpedoes and the heavier weapons used by Archer's Enterprise, hence why she only has weapons dating from Enterprise Season 1 and 2, and probably those were already pushing the ship to its limits.

I agree that Franklin was likely reactivated for the Romulan War, much like the expendable Mirandas of the Dominion War.

Now when Edison became a Starfleet Officer, Starfleet Command may have been hesitant about giving him a brand new starship, and there may have been complaints from other personnel. However, Edison is a public war hero, and asking him to retire may have been scandalous. So, they decide to give Edison a less advanced ship to do what was seen as prestigious: Space Exploration.

Unfortunately, that is exactly the thing Edison hated. I feel like he may have had some Terra Prime sympathies, since all this exploration also leads to more aliens being aware of Earth, and thus risk invasion. Note his crew seemed to be exclusively human, even after the Federation is formed. Also, he is being given a lightly armed exploration ship that was already obsolescent, which further makes him resent Starfleet.

When they got stranded, Edison gets focused on the belief that Starfleet abandoned him, and may have used some of the less loyal crew as test subjects for the life-draining technology. In the end, it was just him and his two most loyal officers (maybe fellow Ex-MACOs who served under him?) and they focused themselves on revenge against the Federation.

(Theory by MikeLima777)