There are a number of reasons why Andrew Wiggins would be a good choice for the #1 pick in the draft.
Wait...isn't this about Joel Embiid? Sure...but we have to get through his competition at #1 first and foremost. And that really is (for the smart GMs) only Andrew Wiggins.
Wiggins has all the athletic tools you could possibly ask for on top of the requisite length to be a formidable defensive beast. He is built a lot like Tayshaun Prince (6'9, 7'2 wingspan) with a slim build...but Vince Carter athleticism. That's an insane combination. Add in his desire to do well on defense (not something you normally see in a young guy) and you've got some serious potential. I'm talking, Scottie Pippen defense potential (8-time All Defensive First Team). That's potential though. So don't get your panties all wadded up yet. There's plenty of time for panty wadding later. His weaknesses mostly result around a lack of an NBA handle, but if he's on our team, he doesn't need a Lebronesque handle...he just needs to move off the ball (huge strength of his) making cuts to the basket and receiving lobbed-oops for easy scores. Well, with a 44" vertical, that's a fairly easy feat to manage. He also doesnt' have a foot fracture.
So, why would you ever consider passing on that kind of talent? Because as good as Wiggins can be, Joel Embiid has the same potential, but on a much larger frame. He's a former soccer (footwork) and volleyball (timing for blocks) player who has only been playing basketball for four years. So, he's raw...but raw guys aren't normally able to do stuff like this. His workout video can be seen here. In this, he looks comfortable shooting the ball, going left and right when on the block and just looks so damned fluid when moving. Not just "fluid for a big man", but actually fluid. His 7'5 wingspan is evident when you see him dunk from what appears to be near the foul line and he's not even jumping high. But he finishes above the rim. His movement makes him very strong in transition where only guys like Dwight Howard (and athletic freaks in that mold) are going to be able to compete with him getting down the floor. His size and fluidity enabled him to shoot 71.4% at the rim. All of this stuff can be shown in greater depth with Draft Express's video profile. If you're not familiar with them, you are doing yourself a disservice. Their videos aren't just "highlight" videos. They actually break down all of the players primary strengths and weaknesses.
If you do a side by side of Embiid and Wiggins, their strengths and weaknesses say some very similar things. Both have great potential on defense (though Wiggins has a head start). Both are highly mobile (particularly when compared to their positions) long athletic freaks. Both have strong offensive upside (this is where Embiid actually starts to gain some ground on Wiggins). Both need to get stronger if they're going to compete at the next level (as they both struggled against it.) Where Embiid starts to shine vs Wiggins is his ability to actually play some offense already. Wiggins isn't ready for anything other than transition points and dunks off of cuts (and the occasional jumper.) He's certainly not creating for himself, let alone anyone else. Embiid can actually score already from a variety of ways...and is a willing and capable passer. Yes, he makes the occasional dumb pass, but he's not a PG. (He's better suited for that than Wiggins is at this stage in their careers though. LOL) Hyperbole folks...no panty wadding yet.
Wiggins is almost the exact opposite of NBA ready than Embiid is. Wiggins is expected to struggle on O and thrive on D. He's a wing who will struggle to create for himself and others. They're really weird like that. But it's all good, because Embiid was blocking shots at a pretty good rate. He needs to work on defense (what young big doesn't?) but he's already showing impressive instincts for it. Add it all in and he's basically the complete package. A package with a pretty bow...that is crinkled. Crinkled with Spondylolysis. What is that, you say? It's a stress fracture in the back. But all stress fractures are bad!!! OH NOZ!!!! Except...not all stress fractures are the same. There are plenty of links out there that talk about Embiid's injury and what it means. Andrew Bogut, Andre Drummond and Emeka Okafor have all had it. Only Bogut went on to have another back injury, and his doctor said it wasn't likely to be related. The other injuries that they've had were not related to the back injury in any way.
Preventing a Recurrence
Spondylolysis is a condition that will recur if you overstress your lower back. The main reason it is thought to recur is due to poor muscle control or insufficient rehabilitation. Fine tuning your back mobility and core control and learning self-management techniques will ultimately help you to achieve your goal of safely returning to your previous sporting or leisure activities without back pain or sciatica that is commonly associated with spondylolysis and spondylolisthesis.
So basically, if the one major reason why you are scared of Embiid is his back injury, there isn't really enough medically to go on to justify those fears.
Add in the fact that you're talking about taking a wing who struggles with shooting consistency, dribbling and passing over him (for all of his athletic talents, those are flaws that are hard to get over), and it would be very tough to take Wiggins over a healthy Embiid (a guy who doesn't struggle at the rim, can finish with his left and his right hand...and can block shots.)
If you want Wiggins for purely basketball reasons (and you have a preference for long athletic wings over long athletic bigs) I get it. We'll have to agree to disagree on what's important, lol, but that's alright by me. But if it's concerns for medical reasons, you don't really have a solid leg to stand on. Embiid has the potential to be a two-way center of epic proportions.