We do technically have quasi-connectivity. It just doesn't function to the full extent that it does in PC. For example, pistons don't react to it at all. This makes secret rooms hidden by double piston extenders pretty tricky to wire. Or in my case, I tried to build a redstone torch key upon beta launch. I got nothing out of it.
Now, things such as redstone lamps and dispensers, on the other hand, do in fact function to quasi-connectivity. And don't forget, running power into a block, then transmitting that power to the other side, is also due to quasi-connectivity. So we can't actually say we don't have it. It's just a bit limited. But regardless, adding that particular feature is still a good idea.
Quasi-connectivity in MCPE would not only be greatly accepted by new redstoners, but it would make MCPE better compatible with Java versions and Java servers. I, for one, would love to play on my win 10 PC with my friends on their xbox and mac. The xbox one seems to be getting closer and closer to a goal of pretty much being the same game as on Java, and I want to see this with pocket/windows 10 edition. On top of this, with Quasi-connectivity, redstone can take up far less space for the same functions, and when building, doors, for instance, it helps make the redstone fit better in the wall, and compact redstone is always a good thing.
On a side note: Pistons are too slow. The ever-favored 2-4-0 method for double piston extenders don't work. In stead of needing just 2 repeaters, you need up to 3, and it's noticeably slower. Just a small beef I got.
P.S.: Maybe have the ability to craft pistons with quasi connectivity. That might be a cool idea. Maybe in stead of using an iron bar, use a gold ingot and the piston will be non-quasi, just to stick to the original recipe for old pistons, or something. Heck, non quasi pistons in Java Minecraft can be pretty cool too. Just so people aren't as jarred as they are when swapping away from Java to the C++ version.
Various bugs have been opened against pistons and BUD (block update detector) powering / quasi-connectivity not working. They have all been closed as "work as intended". Unfortunately this breaks compatibility with the Java client and all console editions. Various standard redstone devices like the Jeb 2x2 piston door do not work.
MCPE-14664 There is no quasi connectivity
MCPE-14740 Pistons do not bud power other pistons
Please add support for to use pistons as bud devices.
Maybe the connectivity of the redstone used is faulty.
BUD system constructor is imperfect resulting to power sourcing in PE mode via redstone devices
I agree quasi connectivity should be added. Or you could at least try fixing the predictably of bedrock edition redstone, because there is little consistency when it comes to redstone and redstone contraptions. That makes it excruciatingly hard to do redstone contraptions that actually work 100% of the time. Just something to think about mojang.