I would play same as now, max. 2-3/day, just would have more variety to select the ones I like...
Having said that, the problem would be that they fill up extremely slowly (would take weeks), which brings 2 issues:
1. now you can see scores from previous days and have a clue what score you roughly need to have a net win, not to lose, or whatever milestone each person has... If it takes 2-3 weeks to fill up a RG and stats are available only for the last 7 days, for most courses it would be largely impossible to have any (at most 1 instance...)
2. since there would be such a long delay to get prizes, people would need to start with a lot of credits in their account (or wait those few weeks) to pay for all the starting fees while potential prizes are in waiting...
So for these reasons I think this suggestion is impractical.