It's not necessarily that the league is trending away from 7-footers. It's that the league is trending away from slow-footed 7-footers that can't stretch the floor. You can go through every team's lineup and see the trend.
Brooklyn - athletic shot blocker
Boston - they've got Baynes out there taking 3s
Philly - Embiid takes threes + he's a freak
Toronto - Valanciunas now takes 3s, but pushed to bench
New York - KP
Milwaukee - Brook takes threes now
Indy - Turner takes 3s
Detroit - athletic shot blocker
Chicago - I don't know what they're doing here
Charlotte - one year of Dwight was enough
Orlando - Bamba and Vuc both stretch the floor
Atlanta- I guess Len?
Miami - Whiteside holding it down... for now
Washington - another Dwight experiment
Utah - athletic shot blocker
Denver - Jokic is a freak + a shooter
OKC - athletic shot blocker
Portland - they've got Nurkic shooting 3s
Minnesota- KAT
LAC - looks like Gortat
GS - Boogie, if healthy, is a freak + shooter
Sacramento - no clue
Phoenix - Ayton will probably stretch before too long
LAL - JaVale (lol) but experimenting with super small ball
Houston - athletic shot blocker
Dallas - athletic shot blocker
San Antonio - no clue
Memphis - Marc shoots
NOP - AD
Basically, if you're a plodder, you have to shoot threes to survive.
You are missing one important thing: ability to throw a basketball from beyond the 3pt line doesn't equate to being a good shooter or automatically making the offense mroe efficient than an offense without a 5 that can "shoot" a 3.
I don't like your list czvo.I think it's inaccurate. A lot of players on your list have other weaknesses and the advantage that you listed isn't all that great unless they can somehow show me a proof that shows their offense got much better with them shooting 3's. A big that can knock down wide open 3's from the corners is a great weapon, but mindlessly taking 3's above the break break is -EV...especially if he can't/unwilling to attack off the dribble and either finish or facilitate.
Tons of bad 3pt shooters on your list, and I guarantee you that if Zizic is developed right he will be taking corner 3's in no time. His FT form and percentage is elite for a big.
Now as far as the weaknesses of other centers on this list. You got Jarret Allen here. The guy has no offensive game other than being a roller and a lob target, is a terrible rebounder and gets dominated by stronger centers. Kanter(a plodding big) just dominated his ass. There is a much bigger chance Allen never fixes his glaring holes than Ante not being able to develop a shot(though again, I don't think it's a neccesity).
The ability now to attack from the post because of this freedom of movement is absolutely enormous for efficient and aggressive centers like Zizic. Players that can finish like that and shoot FTs at such a high percentage is a gift. You can't foul him because he will probably convert both FTs, so what can you do to stop him? double him? that's what Zizic will need to work on..passing. And I guarantee you that whatever those stretch 5's of you are doing, Zizic's .PPP will be higher if he gets a chance and be featured in the offense..especially in the playoffs when the game slows down.
Now you mentioned Dwight. Why isn't he considered an atheltic shot blocker? he is one. The reason he didn't work out was because he was an inefficient post player and a terrible FT shooter and he demanded a lot of touches. Zizic is great at both.
Anyways, there is no reason to not play Zizic. And I guarantee you that he has what it takes to shoot 3's, because it looks like you put it as a requirement, so rest assured.