Benefits of toe grips/toe straps
The main disadvantage to either toe clips or (even moreso) clipless pedals is that until you get used to them you're likely to have a few rather inelegant falls (like pulling up to a stoplight and just falling over).  There are other cases where they can contribute to falls (or exacerbate falls that would have occurred anyway), particularly in off-road conditions (which is one reason that off-road bikers often don't use them).

To me (being partly disabled) the main advantage is that I expend less energy keeping my feet on the pedals.  This isn't as trivial as it sounds: Without some sort of retention system you must constantly work to keep your feet centered over the pedals -- get off-center and your foot slides off.  Of course, people mostly manage this unconsciously, but it still takes considerable effort/energy, especially when you're tired or struggling against a hill or headwind or whatever.

The ability to "pull" on the pedal and gain energy on the upstroke is probably not significant in the general case, but can be important when you need a brief burst of power/torque.  More important, and somewhat related to the previous paragraph, is the fact that you can extend your power stroke slightly, beginning a few degrees earlier and ending a few degrees later.  You don't get more peak torque, but you do get more energy per unit time.