Lilmod,
Those poskim that hold that abortion is mutar in situations such as mamzeirus or severe genetic illness do not hold this way because of the emotional health of the mother qualifying as life-threatening. They don’t require there to be any danger to the mother for abortion to be permitted.
Rav Moshe paskens like the Rambam that abortion is retzicha. Rav Moshe is therefore very machmir on this issue. Other poskim, most prominently the Tzitz Eliezer, pasken like Rashi and Tosafos that abortion is not retzicha (the exact nature of the issur is a lengthy discussion).
Hopefully, none of us will ever be in a situation where they have to ask such a shaila. But if, G-d forbid, someone is in such a situation, it is important that they know that there is a shaila to ask.