[Point System] In tournaments, should playing with black be worth more than with white?

I couldn't find a discussion on this topic, so I'm starting one. I have been wondering if tournaments should give a greater value to play with black. It seems that the obligation to win should fall on white, while black fights primarily for a draw.

I'm not sure the suggestion below works. There might be a better way for giving black a handicap. The main question here is whether black should have a handicap in the first place.

Having said that, this is my current idea. Instead of the current 1-0-1/2 (W-L-D) point system, I came up with this alternative:

White: 2-0-1 (W-L-D)
Black: 3-0-2 (W-L-D)
--
White wins: White 2-0 Black
Draw: White 1-2 Black
Black wins: White 0-3 Black
[Note: I have doubled the points just to make it easier. Ultimately, black would get a 0.5 bonus when either drawing or winning. In other words, basically, the points for white doesn't change (the ratio remains the same), but black has a 50% increase in value for wins and 100% for draws.]

If playing black should indeed be worth more, does my idea work? If not, what would be a better way of giving black a handicap?

In tournaments, usually you alternate between both colours in rounds, so it's balanced. There are also tiebreaks which favour black, and armageddon

Common consensus is that chess is a draw and that black is OK.
Your scoring system would thus largely favor black.

why would you do that?

I've checked it, and it doesn't  work. It's better to draw all matches than winning with white and losing with black (3:2). That's not what I wanted, but it's what I did. It's obvious now that I've seen it.

Back to the board, I guess...

Thank you all for your replies.