Maybe there are some players with multiple rounds in 12h, but I would guess for most players it does not change anything.
A level 1 bear is a little over 14 hrs so anyone who is newish won't get a second round. However they also really won't benefit anyway. I think the better question is how many tourny rounds or spire would you need for this to be beneficial. A pure gut feel from me is:
Tournament
- 6 provinces or less - Don't waste your time on this, those are a practically free
- 10 provinces or less - also highly unlikely to derive much benefit due to the minimal losses
- 10-20 provinces - ???
- 20+ provinces is where it is likely starting to really provide a benefit and the more you do the better the benefit
Spire
- First section (not level) - waste of time as those are super cheap
- level 1 - If you are suffering bad losses but the pain would be short lived. Even small towns can cater this sustainably before too long
- Level 2 - ??
- Level 3 - Due to high squad sizes and multiple waves the most benefit from spire would be here
Of course, anyone who mostly caters gets no benefit from this and it has been stated at least for tournaments that the majority of provinces are catered. So this thing is already targeting a small number of the player base and if they are keen enough to fight enough to get benefit from this they are going to be keen enough to target a timewarp and/or bear when opportunity arises and/or use instants to help maximise the use of this.
The math on whether using this or just feeding a brown bear again or another use of pet food is also highly fluid depending on the player and their town/strategy. I think a lot of people will get it as it is a "shiny new toy" more than any great concern about how beneficial it will be to them individually verse other options.