Continued good thyroid production depends on sufficient carb and protein intake, and cutting calories too low will impair this.
As opinion, getting more caloric deficit with more exercise doesn't impair metabolism, at least if it's done where there isn't an excessive amount of excessively intense work.
As an example of the extreme, Ranuph Fiennes and Mike Stroud dropped about 20 kilos, which I remember as being nearly all fat in the case of Fiennes, in crossing Antartica in 90 days, dragging heavy sleds the whole way. That's about 3.4 lb of fat loss per week.
With pharmacological assistance, 3 lb per week of fat loss is commonly obtainable.
I don't really understand how it could happen but there was a 4 week period where I dropped about 12 lb of fat completely unintentionally with Anaconda and MAG-10 and some rather extreme weight training (I was doing my own 5-3-1 derived program but hitting heavy lower body exercises 3x/week not 1x, doing 3 such exercises each time not 1, so 9 times the volume Wendler would have wanted, and doing them as 8-6-4 not 5-3-1. My knees gave out, otherwise it was a tremendous success.) No pharmacological assistance either.
I think about 3 lb per week is the reasonable practical limit on a sustained basis. It's possible though on a given day to exceed that rate.