I would suggest an additional reason (besides the “appearing like a kofer” problem), based on the Abudarham (Seder Shacharit shel Chol, p.115). Perhaps when it comes to a blessing of thanks, it is insufficient to “ride on the coattails” of another. Instead, one must be proactive in offering one’s own prayer of thanksgiving as well.
The Abudarham discusses this idea in explaining why the congregation says Modim d’Rabbanan instead of the usual one-word response, “Amen.” He writes as follows: “And when the Chazzan reaches Modim and bows, the whole congregation should bow and recite their ‘hoda’ah ketanah – small thanks’ [i.e., Modim D’Rabbanan]…. It is not proper for a servant to praise his master and tell him, ‘You are my lord,’ by means of a shaliach. Rather, every person has to express with his own voice his acceptance of the yoke of the Heavenly Kingdom upon himself. If he accepts it via a messenger, it is not a complete acceptance, as he can always deny that he accepted and claim, ‘I never sent him as my agent.’”
Since HaGomel is also a prayer of thanksgiving (albeit somewhat different than Modim), it is only right that everyone offers his own thanks.
One might ask, “What connection have I to that person’s deliverance? Was I released from jail? Did I cross the ocean? Why should I say anything beyond a simple ‘Amen’?” The answer is that the Jewish people are all connected (“arvut”). Just as we are required to pray for our fellow in the time of his/her distress, so are we each required to give thanks for the good fortune of his/her deliverance from danger or distress.
(To be continued)