rambam hilchos teshuvu says daven screaming and with tears. in shemos perek 2 pasok 24 ”vayayunchu binay yisrael min haovoda vayizaku votoel shavasom al elokim” right after they scream davining moshe came.
A. There are halachos that shmonei esrei is to be recited silently and not heard by your fellow congregants.
B. Why would you say that is unique to 10 Teves?
If you want to scream in the privacy of your own home, or in shul when there aren’t other people davening, go right ahead… all the more power to you. But not while everyone else is davening around you.
Also let us keep in mind, about EY, the pasuk Bereishis (42 21) one said to his brother. But we are responsible on our brother that we saw his pain as he begged us and we did not listen that is why this tragedy comes to us.
Davening very loudly is an acceptable practice in Karlin Stolin chassidus and others as well. The OP didn’t say it was during shtille shemona esrei. If it’s not your speed then don’t. But don’t castigate those who do. And he’s right it’s a befeirishe possuk.
We find by Eliyahu Hanovi when he said at HAr Hakarmel to scream louder that Hashem should hear it. It only applies to the shtiler, quiet shmonei esrei having individual kavonos.
Reb Eliezer, quite the opposite. Eliyohu Hanovi told the prophets of Baal to scream louder so their idol should hear it. One who thinks Hashem can’t hear quiet prayer just as well as loud prayer is described by Chazal as מקטני אמנה (Brochos 24b)