I think important competitions need to be rigid. Things like club champs and matchplay champs where you've only got 8 or 16 people playing in the comp, should all be played on the same day. If you can't make it for one of those dates, you shouldn't enter the comp.
If you've got things like handicap matchplay comps going on with large numbers of players then setting a time period that the match must be played within is a good idea.
I totally understand your point and I don’t completely disagree with it, but my opinion is that being flexible is the better option. We aren’t playing for sheep stations here, most of us are members of local clubs and the primary goal is to have some fun.
Not everyone can be available at the same time every week for 3 to 4 weeks so inevitably you end up with scenarios where the players that should qualify for a match play event don’t end up participating. That is usually fine, but when you end up with 5 or 6 out of your top players not playing because of other commitments and not because they didn’t want to play, is that really the better outcome?
What if a few things pop up for players and a player ends up in a semi-final without actually having played a match yet?
In a perfect world I would agree that it should all be played in the set times, but not everyone lives in that world and people have lives outside of golf that they want to live as well. Obviously some restrictions need to be put in place but what issues would you have with matches being played any time during the week with a set close off point? If a match has not been completed by that defined time than a decision will be made by the committee of which player proceeds (or neither proceeds).
Club Championships (for us anyway as its 4 stroke rounds) are different because you play against a field and not just one player so its not possible to do anything but set dates for them.