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In general, if you create collections in this way, i.e., as a single artifact resulting from a series of others, you can't simply add up all the effects, because the new artifact only occupies one slot. The same four tomes of magic are fine as long as they are separate, because you can't use all four simultaneously in battle, but here the combined effect is like that of a single, powerful artifact.
On the other hand, if you make the effect less than the direct sum, it will turn out that the collection will be inferior to the individual components in some ways.
Therefore, I don't particularly like the idea of such collections that combine everything into one slot. But there is an alternative approach in Diablo, where different components are gathered in the Horadrim Cube, and the result is something fundamentally new, not related to the old.
A remarkable feature of classic collection artifacts is that they occupy several slots. Because of the collection effect, an artifact that is not very strong individually could be placed in one of the slots, i.e., there was some competition for the slots, what to wear, whether to collect the collection, whether to collect it completely. But when everything is in one slot, you don't need to think about anything, just collect the bonuses.
How this will be in single-player, I don't know, but in Multiplayer, such things are unlikely to be needed.