Nice idea. But cheating, using engines and proving it would be an issue.
Make chess more-profitable by betting

Not sure about that. Eg chess.com saves all our games publicly (and permanently!?). Say, before anybody cashes in their winnings, run an engine check of their cash games. Especially statistically, engine help would be more easily detectable. Say 50 games minimum per cashout. Also if a "difficulty of any position" type of algorithm could be outvented, and combined with time per move and moves before the moves, cheating would reduce in nondetectability. Perhaps as much as force the cashing players to comment on their own move(s) as to why they played said difficultmost moves. Also as chess.com already does, do not allow engine programs to run on the background during games. Difficulters post game analysis, but worth it. Easiest of all would be centaur chess with money bets. And a legal agreement to pay for cheated money and damages if caught according to said principles and any others outvented.

Make chess more profitable by betting:
- Remove all rankings, face players randomly against each other.
- Add arbitrary bets per game for the winner. A draw evenly divides the pot.
This way, everyone can get the belief of being able to win big money, and as they win more, they gain more cash to play with bigger bets.
So the game offer includes:
1) Time per game
2) Bet per game.
Now we all get rich easy, huh ?
Also doable is betting on other people's games, betting against other players who bet on the same game during the same move. This divides the profits among those who bet correctly.
The betting service takes its share of the profits, say 5% of winnings (or wherever the price competition between service providers sets the share).
have you seen a doctor recently ?

At your local bar, are the bets large or small change? I think that the OP is talking big money!
I've seen $5 bets in the parks, but one person wins most of the money and he is dependent on a steady flow of new opponents.

Haha in fact I had a meeting with one today. Does this information help you stay on topic more?
It helps me be more concerned for your sanity
"Remove all rankings"...... so we have no idea how strong our opponents are, yet we get no odds ?
You have a very strange idea about how betting works.
"Now we all get rich easy, huh ?"..... hahahaha ....only governments and central banks own printing presses. The rest of us share whats around. We cannot "all get rich" !

Have a look at a spread betting site. This is where people who actually think they really know about how to bet place their bets. Look at the results which in the UK they are obliged to publish.
86% of folk lose money on a 1 year horizon
1% of my winnings to a provider (you I suppose). haha go swivell
Make Internet chess profitable by betting:
- Remove rankings from automatic opponent selection: face players against each other by bet size per game.
- Pot going for the winner. A draw evenly divides the pot.
This way, many people get similar excitement they get from Internet poker. Of being able to win money or lose it. If they win more, they gain more cash to play with bigger bets against better players. Lose, move back to smaller plays.
So the game offer includes:
1) Bet per game (this idea)
2) Time per game (the usual)
Now we all get rich easy, huh ?
Also doable is betting on other people's games, ie betting against other players who bet on the same game. This divides the pot among those who bet correctly.
The betting service takes its share of the profits, say 1% of winnings (or wherever the price competition between service providers sets the share).
This may begin pouring in more money for chess, increasing player amounts. Also people get to play higher-skilled opponents more easily, especially if playing bigger bets. Same as in Internet poker.