For some people maybe not. A video would be far more stressful for me. I'm sure my voice would be up an octave (along with my blood pressure) trying to get the recording just right. Speaking aloud is also not my forte.
One benefit of a cover letter is it is easier to re-use the base story and update the details as appropriate. Unless you want to spend time editing (which depending on your skill impacts the quality) you have to re-record the whole thing.
I find motivation letters to be stressful too and an emotional rape 99% of the time (I just want a job). Hence my question, a video would be just a tiny step lower in happiness compared to a letter.
One benefit of a cover letter is it is easier to re-use the base story and update the details as appropriate. Unless you want to spend time editing (which depending on your skill impacts the quality) you have to re-record the whole thing.