What's wrong with the concept of "there's a thief fleeing from a neighbor's house, we're going to confront him and try to stop him from getting away before the cops arrive, and just in case he's armed we'll make sure we are too, so we don't end up dead"
That seems fairly sensible, legal, rational, and not infused with racist hatred or bloodlust or anything. No?
1) sensible? Value judgement. I won't argue it, for the moment.
2) legal? No. Just no. And that's the problem. It isn't legal. Well, it could be, if this situation was exactly as you described. It would be legal to follow him. It would be legal to demand that he stop. It would be legal, in some states, to carry a firearm with you to defend yourself in case he is armed.
It would NOT be legal to make use of that firearm to effect the other, otherwise legal, ends of confronting him and trying to stop him.
That isn't legal, and that is why the McMichaels, Travis at least but probably also Greg, are almost certain to lose this case.
And of course, your description begs the question of Arbery's identity as a thief, but legally, it's insignificant. If he was a thief. If he was not a thief. If he was believed by the McMichaels to be a thief. Legally, none of that matters. In any of those cases, it is illegal to confront him by threatening him. That threat is the crime of assault. If that threat involves a deadly weapon, it is the crime of aggravated assault.
So, to reiterate, not legal.
3) rational? Again, a value judgement. That word isn't always used precisely anyway. Regardless of whether it would be considered rational, though, it isn't legal.
4) Not infused with racist hatred - Unproven. It is not inherently racist, but many incidents would be racist. Any specific incident may not be racist, in the same way that any specific death by lung cancer cannot be said to be caused by smoking cigarettes, even if the deceased smoked cigarettes.
Now let's return to sensible. Should a person be allowed to use and/or threaten to use deadly force while attempting to catch a person they believe to be a criminal? In my opinion, the inevitable consequence of allowing that would be an awful lot of killings of innocent people. Some of them would die as a result of mistaken identity. Some of them would die accidental deaths when the deadly force is used incorrectly. (i.e. sometimes, some yahoo playing amateur cop is going to fire a bullet that misses his target, and hits someone else.)
In my opinion, the citizen's arrest law is sensible, saying that detention of suspected criminals by private citizens may only be done if a certain set of conditions has been met. Neither your description above, nor the actual circumstances involving the death of Ahmaud Arbery, satisfy those conditions. In other words, I think it is quite sensible to prohibit the use of firearms in the manner used by the McMichaels.