Is it only because it would "look bad on MI5" if people like that worked there? Seems like such a trivial thing to immediately take a stand against and get rid of as soon as you notice it, rather than trying to hide
The continued loyalty of their other employees, a significant proportion of whom also enjoy using their MI5 role as a tool of coercion?
Something like someone who did know him as his secret identity would see his face, hear his association with MI5 and go “Wow Dude! Turns out ‘Niegel from Birmingham’ wasn’t really ‘Niegel’ at all! Didn’t he introduce us to Tommy as his old childhood friend? Maybe we shouldn’t trust Tommy anymore either. In fact why don’t we dangle Tommy from his ankles until he confesses?” So revealing that this miscreant is MI5 could put the life of other agents in danger too.
Or alternatively it can be about protecting some method. Like this terrible person introduced a bunch of criminals to a “secure chat” application, and you don’t want them to think it is not as secure as they think. (Obviously the names and particulars are wild guesses with no basis in reality.)
Not saying it is a great argument, but that is how these kind of agencies think sometimes.
Because people like that are useful to get inside organisations full of other evil people and prevent those organisations doing even worse things.
I hate it, but that is the logic.
"I am ready, Sir!"
"... in some violent, right-wing militia..."
"Oh, I'm way ahead on this assignment!"
All of these things together make it so that the immediate reaction to any apparent wrongdoing is to close ranks, tell nothing to outsiders like the police or prosecutors until some boss decides otherwise. And that boss will of course weigh any such decision against the risk that any minute secret might be revealed in an investigation, that any agent might lose a tiny bit of confidence, etc - and likely will brush it off and apply some paltry administrative penalty then move on.
By keeping him out of jail, Mi5 stood to gain more intelligence