It's a simple reasoning for several reasons.

1. Players complain: It's an NA thing. They don't want their epeen hurt. They are falling behind other players because they can't get on in those few hours to collect tomes and do content during that narrow window while others can. This means they can't get things quicker, and they can boast their superiority to other players by standing around with gear they shouldn't have until the second or third week in. If they can't access the content in that narrow window and get extra stuff, then no one should be able to.

2. Congestion: Everyone rushing in at once to do new patch stuff, max tomes, and do things before the weekly reset can cause 90k's, crashes and such. This is especially true when it comes to high pop serves like gilgamesh and balmung. The entire data center can suffer.

3. SE wants to extend content for as long as possible: 3.1 has to last at least 3 months. Major grinding content should take about 1.5-2 months. Opening up the servers before the weekly reset would kind of kill that. Servers open early, everyone grinds. Weekly reset hits, everyone grinds again. So within a few hours, people will have 2 weeks of progress before the first week has really gotten started. That's a half a month's work of progress. By holding off the patch until after reset, a few hours turns into a full two weeks.