There are a few games that I have seen that definitely could use a video tutorial packaged in the box. I don't think you will see it become a common practice, though, because I think it would put people off if they saw a video tutorial came in with the game. Many people would see that as a red flag that it's super difficult to learn.
Agricola - My fears of teaching/learning this game being difficult have passed. At first, I would make new players watch at least half the video with Scott. It always had an adverse affect. I'd get comments like "jeez, if i have to watch a video, it's too complicated."
I recently introduced it to my cousin and his wife, and we even made them play with the cards their first time (which isn't recommended). They picked it up very fast and his wife even came in second place. The key to learning Agricola is to just learn what gives you points at the end of the game (i.e. lots of variety) - and how a turn order works (Super easy: place a family member, do the action, done) and harvest - after about 2 rounds of play you'll have the game down.
RfTG I really do not think would benefit from a video tutorial. There are some on youtube. This is because the mechanics of how to play can be taught in about 2 minutes. The difficulty people run into with RfTG are two fold. 1) that cards serve 3 different purposes in the game - goods, what the card says, and currency. 2) learning how to read the symbols (note, I did not say memorize them, it's just a system of how to read them).
But I have bought at least one game, blackbeard, where after reading the rule book I wish I had a video to watch. I have never played it and don't want to. I want to sell/trade it after reading the manual.
Edit: Some games got played yesterday I should report:
Indonesia - my friend brought this over. He imported it for $90. It is fun, but gets really math heavy towards the end which makes my eyes gloss over. As all the reviews mention, the map art got out of control and sacrifices functionality.
Ra- This was like my second game purchase after getting into Euro games, after Puerto Rico. A fantastic game. I have not played it in 2 years, but I was reminded why I love it so much. A tile auction game and set collection game. Can't recommend it enough -- but it may be out of print.
Power Grid -- Had my first 5 player game of this and it went really well. The two new players we introduced it too (my cousin and his wife again) got 1st and second place, bastards. Power Grid definitely grows on you each time you play it.
Witches Brew - Already covered this before, but it really is a great light card game. The only downside is it's price. $26 is a little steep for a card game. But it does come with some neat chits.