[ALL1N]

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Think! If calling increases in value as you add bets to the pot then the value of seeing the same amount of cards for cheap also increases as you add bets. If you raise for a free card when you're getting exactly the odds to peel the flop you've basically gained nothing. Getting cheap cards in large pots basically equates to the EV happy dance. Peeling does get cheaper in big pots, but free cards get way better than peeling. What's better, 10:2 or 10:3? Can we also see how the bet saved in a 20:2 vs 20:3 example is more valuable than the previous one? Yes we can.

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So this is your logic:
-calling increases in value as the pot gets larger
-therefore, taking a freecard increases in value as the pot gets larger
-therefore, as the pot gets larger, taking a freecard becomes more valuable than calling.

The truth is that the value of freecarding vs calling is the same regardless of pot size, since it deals with only the bets which go into the pot, and not our probability of winning the pot.