Devil's Advocate: If the consensus holds that staying internal is that much better than switching jobs, to the point that it makes no sense to take the risk, then you, being known to your employer to be interested in making a move, are now vulnerable to exploitation by your employer.

Figuratively, The Move has become a dangling carrot that they know you will follow thru happily just for a bite.

Not saying this will 100% (or any% really) happen --- elusive as they seem, decent middle-upper management do exist --- even then, you would be in no position to refuse tasks that would only serve to distract you from your goals. Also, your employer's time frame in mind for you might be e.g. 5+ years, and they may or may not communicate this expectation honestly to you.

Having both 1st/2nd-hand experiences of dangling-carrot-equivalent events, I must say that it's very important to be comfortable figuring out what is the actual expectation from the above, and have actionable plans. It is awkward, but at the end of the day you have to know better to avoid getting distracted.