After discussing some Shul situations with my Rav, I was marinating an article on Tircha De-Tzibura. I Googled the term to get the best transliteration, and lo and behold an excellent article was recently published named The Halachic Principles of Tircha De-Tzibura. Please go read it, I’ll wait till you come back.
Conceptually, Tircha De-Tzibura is any unnecessary delay in the service. The question than becomes what is an unnecessary delay. Let’s say that in a given Shul, Mincha usually takes between 10 and 13 minutes, and the person who wants to daven from the Amud will take 15 minutes. Should he forgo the Amud to prevent Tircha De-Tzibura. My Rav says that in this case you should not daven as you can see from the halacha that even small time delays are considered significant in this context. So the Nu, Nu choir does have a halachic leg to stand on.
One problem is that the time usually taken in a given Shul for Shacharis, Mincha and Maariv is not always so clearly defined and/or publicized. The best thing to do in those situations is to ask the Gabbai for his understanding of the time parameters, and if you can’t abide by them, then you should’t take the Amud.
Another situation. What if the you’re in the Shul where Mincha takes between 10 and 13 minutes and your capable of davening fast. Do you have an obligation to minimize the time or are you ok as long as you’re under 13 minutes? In this situation my Rav felt that there was no halachic obligation to minimize your time.
From one perspective davening is often a game of minutes, and if you want to avoid the delay of game flags you need to know how long the 30 second clock is set for and how long it takes you to daven from the Amud. If in doubt, it might be best to sit it out.