Prophet is great and we use it for multiple models in production at work. Our industry has tons of weird holidays and seasonality and prophet handles that extremely well.
We also used it at my previous job. Yes it does handle that well, but it was also simply not as correct as we would have liked (often over adjusting based on seasonality) even with tuning. Prophet was probably the right choice initially though just on how easy it is to set up to get decent results.
This is sales research, and after "CAGR in a GSheet" FB Prophet is what's going to be most recognizable to the widest base of customers.
FWIW seems like the real value add is this relational DB model: https://kumo.ai/research/relational-deep-learning-rdl/ The time-series stuff is them just elaborating the basic model structure a little more to account for time-dependence
I would believe those are some of the better options and definitely a useful benchmark.
1. How do you go about finding the "absolute" best when you go to a city
2. What does this have to do with the GP's question?
L1-regularized autoregressive features, holiday dummies, Fourier terms (if suitable in combination) yield lower test errors, are faster in training, and easier to cross-validate than Prophet.