First, we need to stop looking at this through a "VS Battle Wiki lens". Things like "Tiers" and "Attack Potency" are our terms and don't exist in Bleach, so we need to look at things through a "Bleach lens". Why are the feats that we're discussing from the OP happening in the first place.
Aizen says "Humans can't sense my power because they can't sense spirit energy. But their spirits are unable to withstand my power."
So Aizen's power, AKA his quantity of spirit energy, is having an effect on these humans because they can't withstand his power.
Why can't they withstand his power?
Based on Aizen's statement, the logical conclusion is that their spirits are too weak. They have X amount of energy and that is below the threshold needed to survive in Aizen's presence. This is fairly straightforward to accept for me because we've seen humans be pretty much at the bottom of the list in terms of spiritual energy.
We can see this effect of "withstanding power" in the other example I provided in the OP. Don Kanonji, though he possesses a weak spirit, is not so weak that he can't withstand standing in Aizen's presence for a minute before breaking down in the might of Aizen's passive spiritual energy. (He's not close enough for him to be erased, but close enough for other effects to occur)
So possessing higher amounts of spiritual energy logically makes an individual more able to "withstand Aizen's power".
So if Humans (and others who are weak enough in terms of spirit) can't withstand Aizen's power? They get their existence erased at close range.
If an individual can withstand Aizen's power? Logically they won't get their existence erased at close range.
Now, this isn't about their Tier or Attack Potency. Just because someone can smash a mountain with their bare hands doesn't mean their spirit is "strong" or "weak".
The "strength component" that you mention me talking about isn't to do with their ratings or tiers, it is to do with the strength of their spirit.
As far as I see it personally, there are two options; everyone with spiritual energy gets "Resistance to Existence Erasure" which I don't personally agree with, because I feel that it is misleading. Bleach characters don't resist existence erasure in general. Ichigo and Yhwach are just unaffected by Aizen because their spirits are not weak enough to the point where Aizen's spiritual energy would erase them.
Or we change Aizen's Existence Erasure to "Limited." He only erases individuals and objects whose spirits can't withstand his power. This doesn't mean we look at the characters tiers and say "This guy is Tier 4, so he is unaffected." That's just not how it works.