Why does Lichess use an unusual tournament system?

The system that the site uses heavily rewards streaks, or consecutive wins. Two players could get the same number of wins, but the player who has a longer streak gets more points.

Also, if I understand the system correctly, players who are paired against a player who has a streak can get more points by winning their game then players who aren't paired with a streak player. Why should they get more points?

One typical result is that the player with the highest performance rating, over the same number of games, does not win the tournament! It makes no sense to me...

Performance rating could be cheated. For example someone defeated a 2600 opponent on the first game and decided not to play after that. What would happen is lichess would give him a 3100 performance rating and might win the tournament.

Please note that I said "over the same number of games". Notjana told me that the existing system is so that strong players who join the tournament late can win. I think that this unbalances the tournament and makes it somewhat arbitrary.

At first I thought i can farm tournaments about rating, since people play faster to play more games or go berserk to win the tournament. But I realised, even lower rating players than me dominated me in tournaments. I don't know why. Maybe they are cheating. So, as a 1500ish player, tournaments are pain for me.

Maybe one extra point per game when keeping the streak would be ok, but double points seem too unfair to me

There could also be open and closed tournaments:

open: players can join anytime, with streak system
closed: once the tournament starts nobody else can join, no streak system