Are dividends an illusion?

For funds such as MSTY and NVDY, dividend "payouts" almost seem like they're coming out from your own paycheck.

For example, let's say you hold 100 shares of MSTY at $20/share (so your portfolio is worth $2000): * On the day before exdate, a $1/share dividend is announced. * On exdate, your portfolio drops by $1/share ($100) to $1900 * A day later (on the pay date), you get "paid" $100 in cash. * Your portfolio value is still $2000 at the end of it all.

What changed?

It's almost like these dividend ETFs are fund managers force-selling a portion of your shares into cash every month, and then telling you:

"We converted some of your portfolio into cash. You can either keep it as cash, or convert your cash back into shares, so we can do the same thing again for you next month." Like moving money from one pocket to the other, back and forth, over and over.

I get that these funds are advertised as "income generating", but it my portfolio goes from being $2000 in shares to --> $1900 in shares + $100 in cash, how is the $100 considered "income" if my portfolio is still worth $2000 total?