Edited 1/31 to remove my embarassingly wrong answer.

Simplicity I love your ideas about wormholes. I need to think more about influence flowing through them, but otherwise I think your ideas would be great additions to the game.

I would also like to add Stargates--but let them be easier to do than in GalCiv lore, due to new technology. Imagine building something like a shipyard, perhaps requiring several constructor modules to get the basic gate working. Perhaps more modules / higher techs allow access for larger hulled ships, or higher capacity fleets, or increase transit time. Transit time might be several turns, but on an Immense map it would be worth it. This would radically change strategic movement on really large maps. Creating and defending stargates, at both ends, might become a major issue. For an aggressive race going for a conquest victory on a gigantic or larger map, stargates would be extremely helpful in moving reinforcements to the front lines. 

I support the OP's terminology!  Wormholes as first-class values!  Then I can write a lambda function that returns a wormhole, remote-run it on your PC, and your entire call stack falls into the wormhole!

... but some programmers argue that this has already happened in the past.  From the outside, it's a Big Crash.  From the inside, it looks like a Big Bang ...

So what you're saying is, existence is merely someone backtracing from the crash to determine the root cause.  A noble goal.

In a prior devstream (the one on Dec 12th), they talked about the possibility of players being able to construct things similar to Old School Stargates.  The caveat being that you have to truck a ship to where the end point of the stargate would be constructed.

Just like old times (in universe).

One of the ideas Paul threw out was the possibility of having to put the end points of the stargates on the edges of black holes, which might be where this idea of using rifts to travel came from.

This is just an idea up for consideration, however.

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As for wormholes, I love 'em.  When I purposefully decide to use them.  I use them to contact races long before I would normally run across them.  Mostly so I can farm them for techs.    But I also like to use wormholes to find other civs so I can plan out my colonization/conquest strategy.  It is quite valuable to know how much time I might have to build up my systems before worrying about would-be neighbors sniffing around my neck of the woods.

Then there's the added ability of mapping an area (even if only partially) before I get to it.  

Why, hello Class 21 planet.  Pleased to make your acquaintance.   Oh, what's that?  You're just sitting here, all alone, looking for some company?  Well tell you what.  You just sit tight and I'll design a special colony ship to get here ASAP so we can formally introduces ourselves to each other. 

So once I've researched the surveying tech, I will often send a couple of specially designed ships to fly into a wormhole and see if I get lucky or not.  

It's a strategy that's not to everyone's taste (obviously), but I love doing it, personally. 

BuckGodot, you have a good point there, using wormholes to try to find other races early to better prep and to trade. Think I will try that next time. Thanks!

i like the idea of being able to stabilize a wormhole but i think it should be permanently locked in place. im not sure about the 1-way but that could be interesting as well

Personally, I would rather have both stable and unstable wormholes than only one or the other. However, if I cannot have both, I would rather have unstable wormholes. Do I like having my survey ship thrown halfway across the map and seeing it become unusable for however long it takes to get back? No, but it's one of the few things currently in the game that can actually impact early-game exploration in any significant way, and it can have amusing side effects, such as finding the guys on the opposite end of the map before you know who your neighbors are, or encourage you to build a secondary survey ship to replace the one stuck on the far end of the galaxy. It's one of the things that makes each game play out a little differently, and I don't want to see it go.

How does influence flow through a vacuum?

Worm holes, as naturally occurring objects, are not specifically formed or engineered for travel, safety, or communication.  They should therefore be  various degrees of hazardous intrinsically.  There may also be time dilation effects. Or something more weird, like you could be popped into another universe with different physics.

A range of persistence is certainly desirable, but you should be better of making your own.