Edit 1
This new variant seems... better than Lost City for $4? The gaining effect is net-zero as it affects all players equally (though occasionally it benefits you more). Having to return is isn't much of a drawback as the next Wild City you gain can simply get it back. In some ways, its even a boost as it allows you to play the same Wild City multiple times in a turn. This is way overpowered.
I think this mechanic is sometimes a meaningful drawback. On the play when you distribute cards to each player, then have to put your back, the net effect is to give the other players (but not you) a copy of the card. Also, there would be the occasion when you play this with an already-empty Wild City pile (if someone bought the last returned WC), at which point you would lose your Wild City. Other than that, I agree that it has little effect, so I do think you're right about the strength. On the other hand, the fact that these would quickly be spread out to the players might make the card being overpowered less of a problem.
However, there is a much larger concern (imo). As you point out, by returning one and gaining another, the other Wild City becomes available to be played. This creates the not-at-all remote possibility of an endless loop. If you were able to draw the rest of your deck (or all but 3 cards) and had two Wild Cities in hand, with a number of Wild Cities left on the Supply not greater than the number of players, you would:
(a) play a Wild City:
- draw 2 cards,
- get +2 Actions,
- distribute the remaining Wild City/ies to the player(s)
- return the Wild City you played to the Supply.
(b) play a the other Wild City you started with:
- draw the Wild City you gained with the first Wild City,
- get +2 Actions,
- gain the only Wild City in the Supply (the one you returned the first time you played the card)
- return the Wild City you played to the Supply.
(c) play the Wild City you previously gained:
- draw the Wild City you gained the previous time you played the card,
- get +2 Actions,
- gain the only Wild City in the Supply (the one you returned the previous time you played the card)
- return the Wild City you played to the Supply.
You can repeat (c) as many times as you want. If you have the +$1 token from Adventures on Wild City, you can get as much $ as you want. Similarly, since you get an extra Action each time you do this, if you had diadem you could also have as much $ as you wanted.