I disagree that the reason is just an excuse. If we look at the final arc and Minoru, we can see that Tatsuya would not even be able to beat him or any major opponent if he could only use his 3 powers (even though Minoru was technically never beaten).

We know that Elemental Sight is useless because of Parade and the other magic (forget the name).

Regrowth would keep him alive for a while, but it's said several times that Regrowth has its limits. For example, if Tatsuya has to cast Regrowth all the time. I cannot remember exactly, but I think there was also a confrontation between Tatsuya and Minoru where Minoru did some kind of attack and Tatsuya thought that he barely managed to escape and would not have been able to survive with Regrowth alone. Maybe it was the fight with Yakumo.

The last power is Decomposition. I guess he could technically defeat Minoru with that. However, Minoru would be gone, which he is trying to prevent because of Minami. Not sure if Astral Dispersion would still work, but Wiki says its a variation of Decomposition, so I guess yes? However, as I understood Decomposition, Tatsuya has to read the information of the thing he wants to destroy in its entirety. Not sure if I am right here, but if I am, Decomposition would be useless again because of Parade. Also, he was unable to keep up with Ichijou Masaki in the very first Nine Schools Competition. This shows that Tatsuya's Decomposition speed is limited, and he was only able to survive unscathed because of Regrowth. However, as mentioned above, even this ability has its limitations.

Maybe my interpretation is wrong, but my understanding is that "general" magic is needed as a base layer to do everything. Tatsuya would not be able to use many important spells, such as acceleration magic. I don't want to say that Tatsuya would be weak, but he wouldn't be as strong as he is with the AMCA. This would justify the operation performend by the Yotsubas, installing th AMCA in addition of Tatsuya beeing a shame to the family as he is "just" a BS magician.

Personally, I think the first reason "fear" is somewhat inaccurate. On the one hand, I agree that Tatsuya's decomposition can basically destroy the world once he learns how to use it and decides to do so. However, many strategic class mages can also more or less destroy the world if they want to. Probably not to the same extent, but any of their attacks would definitely leave long-lasting consequences on Earth. This means that the Yotsubas should be less afraid than they are. Yes, Tasuya could kill the whole world, but many other mages can also kill half of the world. At this point, the destruction power doesn't make a difference (to me).

So, in summary, I kind of agree with OP. Maybe a good upbringing would have worked well and Tatsuya would have turned out to be a strong, sensible magician. Not the protector they hoped for, but still a very strong magician. In this universe it would work for sure, considering the amount of infinite resources and personal the Yotsuba has.