The trouble is if you're just idly searching a bit and aren't in a hurry, you might not want your current employer (or co-workers) to start planning to be rid of you soon. At the very least, it might make things awkward.
Its strange but I never worked or can imagine working in such an environment.
When coworkers would learn I'm searching for something else they either understand me and/or try to persuade me not to jump ship. Why should they, lol? And if I go they wish me all the best as I would do to them.