There is nothing stopping you from running a Shadowrun game with no magic or matrix. It is your game and you can choose what to add. The Shadowrun game itself is filled with a lot of rules for everything and I've run into two people that run SR games that have honestly dropped the whole Matrix and Magic systems, relying on other people (me) to know the rules when it comes up. They just don't introduce that element to the game.
But that's talking about he game. If you're talking about the story of the Shadowrun universe, then you are missing key elements of the setting by not putting those things in as flavor. They are almost a staple of what makes Shadowrun it's own unique setting. There's a lot that has to do with Magic, mana cycles, the Great Ghost Dance, Dragons, and Horrors (but that's kinda above anything a normal Shadowrun needs to understand). It might not be common for someone to have magical talent, but it's not rare and it's not unheard of. Hell, they have a character in trid movies named Karl Kombat Mage. They have magic. It's a thing. A dragon runs one of the Big Ten and Ghostwalker kind of runs Denver right now. It's not something you can just gloss over.
And the Matrix is much the same way. The Matrix was something that could have killed everyone if it tried. The first Crash that Echo Mirage had to stop before it got out of hand, the Archology Shutdown and rogue AI, and the Crash 2.0 when everything got reset and the wired Matrix as we know it changed. Now we have technomancers, a wireless Matrix that anyone can access from their commlink, and the Resonance. It's something, again, that's vital to the telling of the story.
All of this is, again, story and flavor. It gives Shadowrun, in my opinion, that little bit of edge that puts it up over d20 or Cyberpunk. And it's OK if you don't want to use it in the challenges and it's ok if you want to limit your characters. You can do just fine with a few mundanes or some cybered up guys. You're not always going to find a hacker with enough skill and good magic skill is hard to come back. But from a story perspective, you can't just get rid of those elements.
Now, if we're talking about pure balance, that's another story. The game makes it possible for people to play hackers, riggers, and mages. I think they do a good job of balancing them and how they're built at character gen, so I wouldn't worry too much. But I can see your concerns about some character types, so if you need help on dealing with them, allow me to give you my impression on them.
Magic is a tricky business. On one hand, they're soft squishies that stay in the back and keep out of the fire fights. On the other hand, many people think of mages as super-powered gods that can sling mojo around and generally ruin someone's day without blinking. This is entirely possible in the 5th World, so that's why corporations and the police enlist the best and brightest of mages to patrol areas with their own magic, spirits, and magical assets. A good counter to a mage is another mage. Liberal use of counterspell, stealth, and a summoned spirit or two can be more then a match for most beginning mages. Don't make it too lethal the first time, but use things like that as a reminder that a mage is only as good as the friends he brings with him to a fight. He can't do everything himself and sooner or later, drain will hit him. And then he'll be useless.
If it's an adept, you are honestly dealing with a street samurai (cybered up character) with the same focus, just with a different flavor to how they do what they do. They cost more then a street sam in terms of character gen, but they don't have the draw back of cyberware and maintenance.
Hacking is slow. Let's face it. If you don't have very experienced players that know what they have to roll, when, and why, you're going to be sitting there for a good 30 minutes as a storyteller runs through a 5 second hacking scene. It's a problem with the system that some people just add as flavor and try not to have PCs made for it. Given that, however, hacking is vital to a group. It's hard to bypass security and computer systems in 2072 and you will come across challenges that a hacker could easily bypass or work around. If you don't like having a PC doing the hacking, set up an NPC hacker and story-book what they do.
Now, I love me some riggers. They are the ultimate support role, in my opinion. They're your wheelman, your overwatch, your network security, and the hammer you drop when you need someone's day ruined from far away. But, a rigger is not a one-man-show. He can do a lot of cool things, but he can't do it all. Drones can only get you so much, and there are enemy hackers and riggers out there that can and will jack your ride, your drones, and your ware if you're not careful. If you have problems with a rigger, again, throw a corp spider at them, or maybe someone with good device hacking. Have the rigger contend with someone trying to jack his drones and he won't hav time for much more.