I think you raise some excellent points.. but those points all have rebuttals.
There's nothing really slower about going through an uninhabited system, and in Alex's map there are several cases in the FS or DC where you have to do it or take the long way around.
Inherently there's nothing faster or slower for collecting a charge from a star whether or not there's people living on some rock that may be orbiting it, true. But there is a ton of difference whether you're collecting your charge through your jump sail, or from a recharge station. You can make 2 or 3 jumps via the latter in the time it typically takes to make one of the former.
Other than the 30ly hard cap for a single jump, distance means less to logistics than time does. You can hop "out of your way" 2 or 3 jumps and get at the same destination just as fast (or faster) than going through the more "astrographically direct" path through a single uninhabited system. And that's before considering the advantages of a command circuit!
Post Scrip: Yes it's also possible to put recharge stations in uninhabited systems. I'd even agree it's reasonable to presume that the Great Houses maintain a handful of them in strategic places to facilitate traffic through their empires. They probably also have some additional stations at classified locations just for military and intelligence use. This is part of why I said upthread that jumpship traffic through uninhabited space would better be left to a referee's rulings on a case by case basis, rather than trying to quantify all the angles via (house) rules.
The thing is that in the case I describe is that most crews won't know to go through an uninhabited system, or even if they do they might not have the navigational data to do so.
Maybe, then again maybe not. Again, answering this question for a given leg of traffic is better left to the referee than trying to give rules to cover.
And in cases where uninhabited systems are likely to be transited normal it's not going to be more dangerous, someone else will be along within a couple of weeks, and that's if a rescue party isn't sent out when you don't show up at your destination
I question that Search and Rescue missions would be a routine answer to jumpships failing to show up on schedule. The lore of the setting seems to imply JumpShip captains routinely don't HPG ahead flight plans. Sure, there is some regular or recurring service (e.g. the monthly shipment of Bantha feed) but how often do we hear about raiders successfully passing (if only at first) as unannounced free traders? And take the example of the
Outbound Light... a major plot point about why it found Clan space but the IS couldn't repeat the process was that it explicitly did not file flight plans. In a universe where flight plans are actually a routine manner of course, the Explorer Corps would never have had that lack of foresight in the first place.
There's also other angles for the unlikelihood of standing SAR practices. Taking ATOW as canon, many JumpShips and their captains and crews are actually independent operators rather than property and subjects of this House Lord or that one. They are independent "Spacers" and while some effort may certainly be taken to discover what happened to an overdue troop transport or megacorporate bulk hauler, the powers that be will be less concerned about noone having seen San Holo or his JumpShip for quite some time now.