The 'on' in my post was a misspelled 'no'. It has no tracking issues.
Sanctuary is different because you want to play it for the + card, so making the Exile mandatory would nerf the card significantly. (Which may actually be an improvement, but the point is, it's a big change.) Your card only exiles, so the situations in which it makes a difference are really rare. I don't think there is an existing card that says 'you may' just for the rare edge case where you flip it with a Herald or something.
So what? It is not like there is any technical issue with it. It is like a very small buff that matters with cards like Herald and Golem and Ghost.
If Hanging Gardens has any problems, it is that it is too weak, not too strong. So why do you argue for nerfing it for no apparent reason?
You may Exile a card is more complicated than Exile a card, which I think should matter a lot more than the difference in the effect.
Looks like you are grabbing for straws to justify an argument which has no sound basis after you got reminded that Hanging Gardens is worded precisely like Sanctuary.
No; I haven't changed what I'm arguing for. I think Sanctuary is a complete non-sequitor.
"Exile a card" is simpler than "You may exile a card". "You must" doesn't appear on the card.
To give you some perspective, Donald X said that his biggest regret about Guilds is that Soothsayer says "each other player gains a curse; each player who did draws a card" rather than "each other player gains a curse and draws a card" because the second is simpler. I wouldn't go quite that far, but I definitely think that in this case, simplicity wins out.
Honestly, I think it's a no-brainer. And more than that, it's a design principle of dominion, not unlike having no terminal +1 Card. Official cards don't say 'you may' unless there's a good reason. Consider Forager, Research, Trade Route, Bounty Hunter, Scrap, Remodel, Remake, Sacrifice, Replace, Stonemason, and the list isn't even complete. All of those cards exile or trash a card, and then get some benefit, but don't produce resources if they don't trash a card. For all of them, trashing is mandatory. Now consider Goatherd, Sanctuary, Butcher, Upgrade, Rats. Those also trash a card, but there, you have a reason to play them, so whether or not they say 'you may' changes the power level. For those cards, it's 'you may' or not you may, depending on what makes sense power-level wise. Then, there is a third group where they have to say 'you may' for tracking issues, like Pooka.
I don't think there is a single official card that violates this principle.