For what anecdotal experience is worth, in the past I quit benzos and SSRIs cold turkey, though not both kinds at the same time. Every SSRI I've tried either stopped working after a few months or never worked at all, and I had no apparent issue quitting. I say "apparent" because both the medication, taken for a number of years, and the abrupt withdrawal might have contributed to my brain fog and cognitive decline.
On the other hand, discontinuation of benzos (not technically antidepressants but not off topic I guess) did really increase my anxiety and mess up my sleep cycles. At that time I could tolerate it because I didn't have a job or other obligations. But eventually, when I had to go back to work, I had to start taking benzos again.
Now, laying off benzos would give me excruciating anxiety and I'm not not sure I could become even more suicidal (think my suicidality is maxed out, or almost) but my existence would become even more unbearable until my paperwork and house stuff gets sorted out.