The Fighter's Guild is not a bunch of thugs. They are an Imperial organization with a 1010 year long tradition and they have higher ethical standards than the Mages Guild. You can only join them if you have no bounty on your head and your infamy isn't too high. The Mages Guild on the other hand will accept you regradless of bounty or infamy.
Indeed, They also have a charter with the Empire, granted to them by the Akaviri Potentate. They were the first guild to be given an official, Imperial sanction in this manner. It was because of the Fighters Guild in fact, that other guilds such as the Mages were also later given the same sort of sanction by the government. http://www.imperial-library.info/content/oblivion-history-fighters-guild.
There also should be plenty of work for the FG in the Imperial City. It the largest city in the Empire, so it also stands to reason it has the largest amount of crime as well. The IC is where all the money is. So it is where the people would be who would do anything to get it, and do anything to keep it. This is borne out in the game since it is the headquarters of an entire organization of thieves whom the Imperial Legion is incapable of catching. There also also goblins living right under the streets, and vampires! The City Isle itself has more than one nest of bandits and goblins, just a short walk away from the walls. Given all this there would be plenty of work for bodyguards within the city. Look at all the "guard dogs" Umbacano has in his manor. Every single wealthy residence ought to be like that. With all the people who go traveling, there is plenty of opportunity for more bodyguard contracts there. The Legion might patrol the roads, but I cannot tell you how many times I found people being chased and killed by the wildlife (especially those Black Horse Couriers). Then there would be all the work that IRL private investigators get, such as missing persons, etc... When landlords have to throw someone out because they didn't pay the rent, I bet they'd like a Nord or Orc from the FG there to prevent trouble. If someone won big in the Arena, having a FG member walk you to the bank would certainly be welcome! Jensine should have hired the FG to deal with Thoronir. Agronak should have done the same to have someone investigate Crowhaven. Umbacano could have done likewise to get his Ancestor statues. Any time there was a big event that needed extra security, like a special showing at a museum, a grand ball, and so forth, the FG would be hired. Look at how huge a business private security is IRL, or the Pinkertons were in the Old West. The FG would be exactly the same. The list of possibilities goes on an on.
The lack of a presence in the IC is something I fixed in my fan fic. In it, the FG is not only a group of mercenaries, but also semi-lawmen, who can be activated by the Empire in times of crisis to serve alongside the Imperial Legion and/or City Guards. Many are former legion in fact. As such the entire FG fought at the Battle of Bruma, and most of them died there. They also have standing rules of engagement to fight bandits and other outlaws whenever they encounter them. This is an outgrowth of their original role as the only form of armed protection people had after the local armies of the provinces had been dissolved. As Teresa learned herself:
"I'm not a criminal," Teresa said. Well, not really she thought. The whole thing with the prison did not count after all…
"I am not saying you are," Tadrose said. "But we have had more than one try to get in. That is why we have this."
The Dunmer woman turned a corner and gestured in front of her. Teresa stepped beside her and saw that both walls of the corridor ahead were covered with wanted posters. The Dunmer woman stepped forward again, and Teresa noticed that the hand-drawn parchments were organized by race and gender as she followed. Finally they stopped at the section reserved for female Bosmer. There Tadrose's eyes carefully sifted through the images, pausing to stop and look back at Teresa from time to time.
"Wow," Teresa breathed, looking over the sea of posters, "you people really are serious about this."
"We have to be," Tadrose replied, "our charter with the Empire requires it. If not we would just be an army of thugs roaming the countryside. Besides, people hire us not only because we can do the job, but also because they know they can trust us not to slit their throats when it's done."
"Oh," Teresa said, "I never really thought of it that way." She had never really thought of who would want to hire the Fighters Guild. But it certainly made sense. The more she thought it over, the more it came as a relief to her. That meant that she would not be surrounded by a bunch of ruthless cutthroats when she joined the guild. If she joined…