I'm not sure how this squares with your other proposal that you can tag players you pick up for cheap off the wire (eg $1 Edwin Diaz). I can't see a meaningful difference between nabbing a cheap Edwin Diaz off the wire and nabbing a $10 Pollock off waivers.
Having read Joe and Miguel's input on the other thread, I tend to agree that the system should not be used to keep salaries artificially low - I like their idea that all players should have to go through arb at least once before you can tag them.
I can see what you are trying to do - to reward teams for doing their research and being the first to unearth the next star for $1 - but I think having too many artificially low salaries floating around the league would ultimately be detrimental (and I say that as someone with a $1 Edwin Diaz on one of my rosters!).
However, having said that - I do think that player's acquired in the main pre-season auction could potentially be tagged at the end of that season before arb. My reasoning is that all (or very nearly all) teams hit the draft in a position to bid on the talent available - whereas in-season some teams do not have the cap or roster space to make a speculative bid on a Edwin Diaz. So being able to tag 'in season' acquisitions rewards teams who are able to shed talent in season (ie not competing) at the expense of teams who need to keep their roster together.
Not sure how clear that is!
I'd be open to the idea of tagging players acquired in the pre-season draft before arb (though I'm not 100% committed to this)
But I agree with the set up in League 100 that players acquired off the wire (whether free agents or cuts) cannot be tagged until they have been through arb