Many years ago, as with today, people would go into a caloric defect to drop body fat.  Back then there was a theory that your body would adapt to the lower calories by slowing the metabolism.  For that reason it was desirable to bump up the calories for a day every two or three weeks.  That would kick start the metabolism and not let the body get too used to functioning on lower calories per day.

Has this theory survived the test of time?

Nothing has really changed.  But most people don't cut hard enough to need it.  "Cutting" is not eating like a slob and taking drugs these days.

When i actually cut,  i did one every 7 to 14 days.

It's probably fine, your body doesn't really think much in terms of hours or days.

Keep your weekly or monthly calorie count in a deficit, and you'll still lose weight.

There is the mental health aspect of it too. If you maintain your 500 or whatever calories below TDEE every day, then Sunday you want a beer and a bagel, just track it like anything else and don't binge like a pig.

A few studies have shown that when people do a fasting schedule, even when they do binge a bit on a feeding day, they still don't eat enough typically to go into a surplus, so that's an option too if your body is good at self regulating hunger levels.

I am pretty sure I was under eating when I did this. But when I dropped from 265 powerlifting to 195 lifting every other day and cardio in between those days, I wouldnt lose weight until the weekend when I binged for 1 big meal. I went through a sting where I would eat a large pizza and wings and the next 2 days I dropped pounds. Because it was working I didn't care and kept doing it.

I probably wouldve done less damage, lost less muscle, and felt better if I wouldve eaten more during the week and not did the one big meal.

I have read what you are referring to many times but I have never researched it. It worked for me but the 6 other days of not getting the right amount of nutrition probably created a ton of stress inside the body I didn't need.

I think most reputable coaches recommend diet breaks at certain intervals. Partially so your body can resensitize and partially for the mental aspect.  

What I found with my weight loss (started at 240#+ in Nov '18, down to 191# in Jan '20), is that I can pretty easily lose weight at a rate of 1.5-2#/week for a while. But once I'm past about 15#, it starts to slow down.  By the time I'm down 20# on a cut, weight loss slows significantly.  So I've been doing 12-week massing phases after each 20# loss.  

I tried to just continue and push past the weight loss plateaus, but without a ton of success.  

Late last year, I cut for 5 months, ended the cut on Jan 31st.  Initially, it was 2#/week. By the end, it was maybe .5#/week, if that.  Lost 25#, but by the end, i was fried.  

Did a 12-week bulk (12#) and have now been doing a moderate cut for 4 weeks. Lost 5# in those 4 weeks, am now as lean as I was at the end of the last cut, despite being up 7# from then.  I feel way better, still feel like I can cut several more pounds without issue.  

The disadvantage is that it's taking longer overall to lose the weight, but it's much more sustainable in the long run.