There are plenty of people who ruin their marriages one way or another and go on to have full careers. If you think we should just let military members, especially officers, especially senior officers, run around banging whoever they want regardless of their marital status, I think you're in the wrong business. There's no law that says you have to get married or stay married. If you can lie to the one person you should be 100% truthful to, then why wouldn't you lie to everyone else?
In the good General's case, being the country's chief spy, having a skeleton like that opens the door for countless issues. The potential for blackmail exists. There's obvious and apparently very real concern that classified information has been leaked. She could end up being some psycho that starts threatening every female you know. She could drive half way across the country shitting herself with the intent to murder people on the other end. It's not just the military side; Lockheed just fired their inbound CEO. (I know you said "this country" and not "this military.")
Like it or not, a person elevated to that level of trust should be trustworthy and they can't expect to be surprised by the fallout otherwise.