Prevalence of Wizards

I can understand why one could get that feeling from the published Realms, because there's so much emphasis on powerful mages. In the same way that New York seen in movies is always being blown up or threatened with doomsday devices or the setting of all-out gang street warfare, but the real New York is rather different. Arcane magic DOES permeate the setting (in the form of the Weave), but it is by no means "commonplace" or ordinary. I would say that perhaps one in every 290 or so people has some talent for the Art (magic), but usually this is a "wild talent," a very limited, lone minor power like an itching sensation when a powerful magic item is very close, or a mighty spell has just been cast in a locale, or is "hanging fire" awaiting activation in a spot the wild talent is standing in. Wild talents are rarely reliable, are usually kept secret, and VERY rarely can be developed, over time, into something a little stronger and more specific.
Perhaps one person in every 400 or so has some limited immunity to some form of magic (lessened damage from fire or cold magic, or increased resistance to mind-contacting magic, for example unless it's genetic and older family members tell them of it, they may never ever discover they have this immunity.
Perhaps one person in every 900 or so has some ability to wield magic (i.e. become a wizard or sorcerer or other sort of arcane spellcaster). Again, they may never discover this - - and if they need training to develop it (i.e. become a wizard), they may never get the opportunity or the funds to be trained (nor might they WANT to; a lot of folk in the Realms fear magic). My estimate of how many people become wizards would be around thirty percent of those who could become wizards (i.e. 3 in 10 of those talented in the Art ever develop that talent). And of course, once you are a wizard, you are also a target. The vast majority of wizards get killed when they are low in power (such as Manshoon's "magelings," the novice Zhents he sacrificed ruthlessly in great numbers), and the great bulk of those who do survive become "hedge-wizards" (that is, they get a little training and do a little experimentation beyond that, or buy a scroll or two, and settle down in a small community to make a living casting the six or seven "everyday useful" spells they know, never wanting nor trying to either go adventuring or try ruling anyone or anywhere).
And yes, aside from the risks of everyone else trying to kill you or capture you and use you as a spellhurling slave, you as a wizard face the inherent risks of magic itself; it's like playing with live electricity at the best of times, and experimentations or any situations where one active spell comes into contact with another (i.e. any duel or fight) are especially perilous.
And finally, in the Realms there are many, many individuals powerful enough to rule, dominate, and even oppress wizards. If you look the root Realms products, such as the Old Gray Box, most rulers are NOT wizards. (It's just that the evil wizards' groups, such as the Zhentarim and the Red Wizards, get all the attention.)
Magic is an inherent part of the Realms - - LOTS of magic. Some of it is divine, some arcane, and most of it is unharnessed, or controlled by beings we don't think of as potential Player Characters. The PC users of magic are few and far between; don't let what adventures focus on give you the wrong view of their real reach and stature. Their REPUTATIONS are huge, but even an active band of them (e.g. the War Wizards of Cormyr) can't adequately control a generally law-abiding kingdom - - and one of the few wizards who COULD rule the world, Larloch, is utterly uninterested in doing so; like many ultra-powerful archwizards, he has become obsessed with the pursuit and perfection of magic, rather than worldly power. (Though you may in future Realms fiction see him dabble a bit in the unfolding affairs of the world.) Finally, like real-world superpowers and "detente," the most powerful mages often develop feuds and rivalries, and serve as checks and balances on each other by opposing whatever rivals try to do.

Ed 9/9/13, replying to a challenge that wizards outpower everyone else