The difference is that if the company pays dividends then the stock price will drop because it represents a claim on a smaller amount of assets. So you can achieve exactly the same effect yourself by periodically selling a small percentage of your holdings. It's like having a big piece of a small cake versus a small piece of a big cake: if you get the same amount of cake in the end then who cares how it's shaped.
If the dollar value of your holdings appreciates by 7% each year and you sell 4% of your holdings each year (by dollar value), you can keep selling indefinitely. (This is, incidentally, exactly how retirement accounts work.)
If you sell a fixed % of your holdings every year (that is equivalent to the % you would get paid in cash due to a dividend) you will never run out of equity.
The difference is that if the company pays dividends then the stock price will drop because it represents a claim on a smaller amount of assets. So you can achieve exactly the same effect yourself by periodically selling a small percentage of your holdings. It's like having a big piece of a small cake versus a small piece of a big cake: if you get the same amount of cake in the end then who cares how it's shaped.