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Small Pairs on early and middle positions
(+1) I'll just add that you can win big pots when you have a pocket pair that connects with the board to make a set. From my experience, these hands can catch your opponent off guard when there is a non-descript board (e.g. 2-4-7-J-K when you have 77 and they have AK or KJ). This dynamic doesn't exist as much with other cards (e.g. suited connectors) because players often notice when there are flush/straight possibilities or when the board pairs to give someone a set/full house possibility. This added element can win some huge pots with pocket pairs and, I think, gives more added value.
Profitability of re-buys/add-ons when allowed
+1 to the question. Just as a note: you've made a rather strong assumption here that your probability of winning the tournament is exactly equal to the proportion of chips that you hold. The inaccuracy of this assumption may explain why your mathematical intuition fails you here.