I think that it's a lazy strategy to put all your hopes of winning in a whole season on a team, it won't give you the interest to critically explore other teams performances. I have my favorite team that I support but when it comes to gambling my money I look beyond favoritism and analyze to know which team that has a better chances of winning. Sports bet is more fun when you're able to analyze the chances that your favorite team has against other teams in the season before placing your bets. It gives you the chance to assess the performances of other teams.
That's true most folks don't usually base one favoritism when betting or gambling rather they will take their time to analyse by checking each teams performance in their previous matches. But I like op Idea of using a fixed amount of money to always gamble like something you can risk that won't stress you to get back . Like some folks fix amount for gambling can be $10 and they won't go above that most time and it's also a sign of self control thighy, because those that don't have fixed budget, always go beyond their budgets most time .
You are right, anyone who bets on a football match will see the history of the team they are going to bet on and it is very unlikely that they will continue to side with a football team of course there will be very little chance that they will be able to win the bet they play.
If someone bets with the money they have previously set and will not take other money back to gamble, then this will of course be very profitable for them and will also be able to maintain the funds they have, because if they continue to take other funds to gamble, it is not certain that they will be able to win the bet and it is also true as you have said that this is part of a person's self-control when betting and not everyone will be able to do so and only those who can control themselves when gambling are able to do so.