It just dawned on me that you're EU and so you're probably being impacted by Faloop hierarchy and Early Access versus Public Access BS.
Seeing things from that perspective, your idea then seems like a better solution because it takes notification control out of Faloop's hands and puts it back into hands of anyone who wants to hunt, not just Faloop's favored and privileged children.
Regarding engaging fights, depending on what you consider "engaging" hunts may never reach that level. Even the SS ranks have a small number of mechanics that aren't difficult to learn. A level sync isn't going to make them all that much more engaging once the mechanics are known. They'll still just be target dummies with higher HP pools in the long run. Most of the fun comes from being part of the "flash mob" that appears to kill them.
Trying to "make the system more robust against griefing" would also remove part of the challenge to getting the SS to spawn. You would effectively create a "can't fail system" instead of a system where there is still some risk of failure. SE has to balance any proactive anti-griefing tools they would create against how it impacts the intent of the content.
What SE's exact reasoning is for the hidden timers I can't say. If I were asked to guess, I suspect it's because they're prefer to not have large crowds of players camping zones for hours at a time when there are other players using those zones for reasons other than the Hunt. Players are far more likely to act when the information is freely given to them than if they have to make the effort to seek out the information. Again, that's just what I would guess.
I don't have any problem with world travel being quicker if SE has the ability and desire to do it. My problem is with players who think that other players owe them time and should have to wait excessive periods so they and more random players from other worlds can take their time and still get credit.
I'm glad for the discussion. SE needs the broader overview of how different members of the community see the content if they are considering possible changes. If SE did decide that change is needed, either I'll adapt or I'll quit the Hunt. Nothing lasts forever.