Free showdown play

[Dazarath]

I see a lot of people respond to threads saying to raise the turn for a free showdown, sometimes when it's not very apparent what the gain is. I've always used the free showdown play in the following situations:
1) I have a marginal hand, and there's a good chance that my opponent is drawing. Therefore, I want to put in 2 bets on the turn to charge him for his draw, but I don't plan to bet the river. Had I just called the turn, I may only be putting in a bet on the river when he hits his draw, so the point of using the play is obvious.
2) I have a marginal hand with a draw, as well as a slight chance that I may have the best hand at the moment. Something like middle pair with a flush draw. I raise the turn, so that I can check behind on the river if I don't improve and only bet if I improve. This way it costs me 2 bets to get to showdown, but I get 3 bets in if I hit.

The second situation requires several assumptions, though.
1) My opponent has to be passive enough that he will not raise the turn or donk bet the river. (If he's the "tricky" type who always loves to checkraise after shown aggression, this is fine as well.)
2) The draw needs to be obvious enough that my opponent will probably check/call if I hit, ie. pair + flush draw, or pair + ace overcard where I raised preflop, pair + 1 card OESD. If my draw is hidden, I'm most likely getting in 3-bets anyways, so there's no point in putting in more while I'm drawing and risking getting 3-bet.
3) The opponent needs to be the type to pay off when I hit.

In some threads, I've seen people suggest the play, even when it seems like there's no difference from just calling down. An example would something like TT on a K722r board where the opponent's play looks like either a weak K or an 8. The way I see it, you're putting in 2 bets if you don't spike a T and maybe 3 if you do river a T (could be 1 or 2 depending on how often your opponent folds).

I guess an argument could be made that for an EV-neutral choice between calling down and raising for the free showdown, game theory would dictate that we choose a randomized strategy. Other than the situations I've described above, is there another reason for the play that I'm completely missing? Thanks to anyone would can help me out with this.

[piggity]

One reason you forgot to mention is that your opponent may fold to your raise on the turn.