I understand the frustration, and while I'm not going to adopt the one-day jump change, I can see the appeal. I do think the rapid (relatively) jump times would change the structure and nature of the Imperium as pointed out by a couple of other posters.
I like the delay, and the isolation it provides. I also like the fact that it makes Travelling a much bigger deal and something that has to be carefully thought out.
Klaus Kipling said:
For instance: there's been a murder on a remote base or outside normal jurisdiction, and the player's boss at HQ calls them in to investigate. Except, by the time they get there, the crime is, at the very least, 2 weeks old...
Or the murder is in a remote outpost in the same system. (Ala Outland, maybe?) Planetary authorities don't necessarily have jurisdiction that far out, but they may want to hire someone to find out what is going on.
Klaus Kipling said:
The player's patron gives them a mission to such and such a planet, a few subsectors away. The trip will take months.
If the patron has interstellar concerns, sure it may take months, but it also explains why they'd hire the players rather than local help. For more local issues, the mission could be in a neighboring province of a balkanized world, on the moon base, or in an unexplored section of the same frontier world.
Klaus Kipling said:
The PC's escape a trap and jump out-system, so the henchmen sends a courier back to the evil nemesis to tell them where he thinks they're going. Except, by the time the nemesis gets the message and jumps in, all he sees is the player's ship jumping out again.
On the other hand, the evil nemesis has a week or two clear out of the system before the PCs return with reinforcements, leaving him free to hatch another evil plan.
Klaus Kipling said:
How long do the IISS wait before declaring their ships overdue for return. A year? 2 years? Scratch that rescue mission then, as the crew will probably be dead long before the IISS starts looking for them.
Thus the low survival rate for Scouts.

This also let's the PCs know that there isn't going to be help on the way...
Klaus Kipling said:
Of course, there are narrative ways around these issues, but they end up being clunky and repetitive, like trying to make sense out of nonsense UWPs.
IMHO, (and I'm not trying to bash you here... I've faced the same problems) you get these clunky and repetitive "solutions" when you try to build a narrative that conflicts with this underlying premise rather than builds on it.
All that being said, I absolutely agree it is a pain to explain the premise to new players, and I haven't figured out a good way to deal with contacts and allies who may be months away...