The price of a thing should drop by exactly the amount of dividend it pays out.
It is like a bank account. When you take money out of it, the balance decreases.
Obviously there are market fluctuations as well, but still.
If a $20 ETF pays out a 20 cent dividend, it will be a $19.80 ETF and you'll have 20 cents.
Is this always the case - even with a broad market ETF?
There will always be inaccuracies, but there are 'market makers' and arbitrageurs that will do their utmost to make it so, yes.
The 'problem' is that the market is always moving so you can't 'see' the exact drop (try looking at a bond fund though - it will rise by 5 cents over the month due to coupons coming due, then drop by 5 cents when it makes the payout).
There are a lot of very wealthy companies with very fast internet connections that will take fractions of cents of value out where there is a disconnect.
Even a broad market ETF? The more actively traded it is the less of a spread there will be. Of course there is the fact of different markets opening for different times, but... Look, if it was possible to make easy money like this (ie, buy the day before ex-div, sell the day of) don't you think everyone would do it... except if they did... they would exactly counter what you're talking about...