Far be it from me to tell people how to play, but I'd advise against the Cage and the Lotus. They're about equal to, or barely better than, many pure culture items that you can craft in the Magic Academy. So you're basically spending something limited (event currency) on something that you could otherwise get "for free."*
Plus, small culture buildings "go obsolete" much faster than nearly any other building (for instance, if you got a Great Auction - 5x5 squares) you could easily keep it around for at least 2 chapters. Less so the case for Flower Cages/Lotus.
Again, not trying to tell you how to play. Lots of people don't have access to crafting, and *crafted items aren't free (there's relic cost and opportunity cost), and your city layout may make lots of the other prizes difficult to place. But just my 2 centers.
Hm, both cage and the lotus give seeds starting from Halflings (lotus is better by the way). These are not pure culture buildings! There are really not that many options for seeds out there, so I would actually seriously consider going for several Black Lotuses.
And I am actually liking BL better than Golden Palaces now - while on paper they have comparable seeds per square, BL is much better from the collection mechanism perspective. GP runs on 24hr cycles with
no early collection. This means unless you time your collections perfectly, you will be wasting some production time.
BLs, on the other hand, have early collection and a huge collection window. They run on 24hr cycles, but early collection is available after 6 hours. So you have 18 hours a day to collect without wasting. BLs are much easier to run 24/7 - not to mention easier to place (marginally).
Might not be very appealing for players with a ton of completed provinces/AW levels who are overproducing seeds in the trader