Yes, the question is - did the electronics die, the motor spinning the disk, the bearings, or the actuator moving the head? (Or did the sealed disk leak?) usually the electronics or the motor die. that means the data is still good. However, the trick is reading it.
If the head “crashed” ie. stopped floating over the disk, then the disk media is all scratched to crap and probably not worth recovering. Ditto if the seals leaked (unlikely without physical trauma) since dust as fine as smoke particles could crash the head based on tolerances for disks made in the last 15 years. Ditto if the bearing failed and produced metal dust.
nowadays, I suppose a fancy lab could replace the electronics or motor and recover the data. I never heard of someone replacing either themselves, I suspect the motor is sealed inside. years ago there were services - still around, I assume - that could attempt to read what they could from failed drives if the head and platters were intact. However, if the electronics were slowly dying, it’s possible they wrote gibberish toward the end. If you want NSA/FBI levels of analysis, that will cost.
The FBI might be able to make use of fragmentary information. Someone with a deep knowledge of file formats might get some usable data off fragments of a spreadsheet file; plain text is the easiest to get useful data from. However, unless a file is recovered intact, it is generally useless to the layman; it’s cheaper generally to recreate the data from other sources. Audio, photos, or video? Again, why bother. (I’ve seen enough corrupt av media - it’ painful to look at) In modern OS’s a heavily used disk would be seriously fragmented, and recovering a decent sized file would involve reading pieces scattered all over the disk.
the freezer trick was famous in the early days of hard disks. If the bearings or something are out of tolerance or motor stiff, it might work. Where it worked around 1990 was disk head alignment. A disk head has a read/write gap. It swings across the platter on an arm. If manufacturing stresses meant that arm slowly changed shape, the head gap would change angle and eventually not read what it had written a while ago. The trick was that cooling would relieve the stress in the arm and change the head angle long enough to retrieve the data.