Mathjack I am pretty confident that most of the people on thread understand that math behind the process, certainly HaHa, myself and Nords do. Mathematically you are correct there is no difference between spending dividends and reinvesting dividends and then selling a fix portion of the shares.
I think what you aren't grasping is that from a practical and psychological perspective it makes a pretty big difference between having to sell X% of your portfolio and having a good deal of confidence that you collect $Y in dividends.
Imagine that a retiree has a equity portfolio that consist of 20,000 shares of VTI. His withdrawal model is the Clyatt method which is each year spend the greater of the 4% of the remaining portfolio, or 95% last years spending. (If I switch to total return investing this is what I'll use). This means he needs to sell 800 shares of VTI put the proceeds in his checking account. So how much does have to spend this year.
Gee well it depends a heck of lot on when he sells.
Jan 4 (1st trading day) $52,480
July 1 $55,504
Yesterday $46,120
Now that is pretty dramatic difference in spending levels.
Ok lets that you decide to smooth out the selling and sell 1% (200 share) per quarter. Now normally I'd want to avoid selling at the end of the quarter because of portfolio window dressing, so I'd pick some dates like 3/15 6/15 etc. However this year selling at the end of the quarter is 5% more income than the middle of the quarter. (Now if you want say I am just going to sell $40,000+ each year than I'll point the number of shares you have to sell each year varies significantly when you sell them.)
Prior to 2008/2009 I had never seen a dividend cut in my life, but after several banks, and Pfizer cut there's I saw 10% decrease in income. Now given that lots of private companies, and latter quite a few state and local governments imposed similar pay cuts on employees I didn't feel too bad.
Overall I think the stability/safety of the dividend income while far below a government or most private pensions, or Federal government jobs, is superior to most sources of income. Probably jobs at most private employers, possibly a bond fund, and almost certainly selling 4% of my portfolio on fixed schedule.
All of this assume that you are perfectly logically investor and won't be tempted to do a bit of market timing when it comes down to your annual/quarter withdrawal. If you are human type of investor you may have been tempted to sell yesterday or on Aug 8th.