I don't quite get it. What is there to panic? Even before you have entered your trade you should have put your stop loss. You know up front how much you are willing to lose. And you are totally fine with the possible loss.
If there is slippage, yes, you may lose a little bit more than planned. But what's the alternative?
How can "sneaking out slowly" be a better option? Say there is a violent move that continues in the opposite direction with respect to your trade for days seemingly without end.
Setting a stop lose immediately is the only option.
Some people say, having a stop loss in your mind (an idea where you are going to exit), enough. No it isn't if you ask me. Precisely because shit scenarios happen.
This has always been a debate among traders. I tend to agree with you.
I know people who operate with "mental stop losses" and I have employed this strategy myself at times. I've found that it makes it much easier to fall into a "bagholder mentality" where you begin rationalizing letting your losses run. You think, "I'll just sell the bounce..." but then, the bounce happens 30% further than you expected! And then you've just broken all your rules and destroyed your account.
Most people are better off using market order stop losses (or limit order stop losses with wide triggers if those aren't available). Just cut the emotions out entirely! If slippage is an issue, you should be spreading your positions across multiple exchanges or brokers, not depending on being able to scale in and out over long periods of time.