Why do we bother with SCRs?
While you may have undoubtedly found a load of principes of operation of SCR vs TRIAC it seems you miss out, at least (but likely not limited to):


The Recovery Time of a Thyristor Type (the family of devices): If your signal might reverse quicker than the Thyristor can recover in the case of an SCR it will still return to blocking state ("eventually"), as long reverse voltages and rates of change are below where it permanently breaks. A TRIAC will just conduct in the opposite direction as well, as it remains broken down until it "relaxes" long enough = The charge carriers "settle down".
Reactive Loads Causing a high rate of change of Commutation Voltage might also trigger a TRIAC to turn back on on the return cycle, due to current and voltage being out of phase. If the current 'turns off' the voltage is high (already in reverse from phase change), this then stimulates the charge carriers in a TRIAC to not go back to rest (blocking state). This is a problem significantly smaller in SCRs. Here a Snubber Circuit may help a TRIAC cope to certain limits.
A rectifier fed inductive load, or very high load current may do the opposite of the previous point: A high rate of change of commutation current, which then causes similar problems. In the case of rectifier fed inductance you might choose to build the rectifier up of 2 diodes and 2 SCRs in stead, to again mitigate the risk. Here a snubber circuit would not help much with a TRIAC.
An SCR may (MAY) at a similar cost be less sensitive to thermal effects on its blocking/off-breakdown voltage, but this depends a lot on the internal build up of the TRIAC in question.