Research the production of the bird on
https://idavis-elvenar.github.io/buildings.html or elven architect. The per tile output for population or for culture or for both is woeful. To this add a 48 hour collection for an unimpressive amount of goods and the bird comes close to topping the list of event buildings that are
inefficient.
This illustrates my point exactly: it depends on chapter and player capability. You're absolutely right that it's not worth the space for production alone in higher chapters, which is why I did not place the Phoenix in my chapter 8 city after consulting ElvenArchitect when the event started. However, I did place it in my newly-chapter 3 city because it is actually efficient at that level: the Phoenix takes up the same number of squares as 4 planks manufactories at the level I currently have. Each plank manufactory currently produces 46 planks per 3 hours, and 86 per 9 hours, so if I run a maximum (for me) production of 4 3-hr cycles and 1 9-hr each day, that means each plank manufactory gives me 270 planks per day. Multiply that by 4 to get the same footprint as the Phoenix (1080) and by 2 again to cover the 2-day production cycle (2160 planks from 4 manufactories in 2 days). In comparison, the chapter 3 Twilight Phoenix, evolved only to level 8, gives me 1716 planks and 993 marble in 2 days, a total of 2709 T1 goods, an increase of just over 20% from what I can manufacture in the same footprint at the moment. That doesn't even take into account the 1 KP, or the population swing of 364 people (that's more than 3 fully upgraded residences can hold; +154 from the Phoenix, -208 from the manufactories) or the culture difference of 396 (+308 from Phoenix, -88 from manufactories), or the savings on gold and supplies it would take to run that many production cycles... It simply is more efficient at this level than the alternative, and would be even more so for a player who got it fully evolved, who does not have the ability to check in every 3 hours throughout the day, or who has a lower boost value.
Perhaps I don't understand the absolute best way to use it but then we were both just offering hypotheticals as to how we foresaw this addition to the game playing out. I'm not saying that I believe it's the answer to new players' battle woes, or that I think it covers for poor choices. I do believe that trading a pet food now and then (which I would have the fragments or relics/catalysts to do, even in my chapter 3 city) for the sake of saving precious time and supplies on retraining troops would be worth it. Maybe if I observed the actual numbers somewhere, I would find that it doesn't actually save enough time to be useful in that way; however, since I already know it can be used as an efficient production option (for however limited a time), my inclination is still that the feeding effect could merely be icing on the cake for a newer player since the bottom line is that feeding it will save
some time and supplies spent training troops, however meagre those numbers might turn out to be in practice, and most new players don't have other pets vying for that same food.
(Edited slightly to make more sense with the post I was replying to.)