Is it permissible to use the phrase "necks bow before him" to express people's respect for or submission to a person, or is it among the forbidden linguistic expressions?

It does not appear that the aforementioned phrase is inherently among the verbally prohibited expressions. However, if the intention is to praise someone, it should not be used due to the blameworthy exaggeration and excessive flattery it contains. The prohibition becomes stronger if it is a lie, or in the presence of the praised person, or if there is fear of temptation, based on the Prophet's (PBUH) saying: "When you see those who excessively praise others, throw dust in their faces."

If the intention is a metaphor for people's respect or submission, then it is a permissible figure of speech. And if the intention is to state a fact, then merely stating the fact is not prohibited. Rather, what is prohibited is the action itself; for the Prophet (PBUH) forbade bowing.