Gee, as someone who has driven thousands of miles all over Europe and the USA in cars with wooden wheels and mechanical brakes, I'd say that the scary factor you are referring to is probably down to poor maintenance of the car, rather than any inherent design deficiency. Believe it or not, a '29 Chevvy is a fairly modern car, and capable of cruising coast-to-coast in a week without any serious drama. BUT... any 83 year old car that's allowed to sit (and basically rot) for long periods of time (and that looks to be the case with the car in the photo) will require a reasonable amount of effort to bring it up to road-worthiness.Here is a picture of my '29 Chevrolet coupe. It is in very good original condition, but I'd rather have something I can drive farther than just around town. Mechanical brakes and wood spoke wheels are scary on the street, let alone putting the backroads between towns.
David has suggested replacing the wood spoke wheels with Coker's 20x4 inch steel wheels, something I'd advise against as it will involve significant (and expensive) machine work to change the hubs to accommodate the new wheels' 5-lug pattern. Why bother? For probably far less expense the existing wheels can be rebuilt; further, modifying the car will lower it's value, not enhance it.
Let me suggest that your car would probably be a lot less "scary" to drive if you (1) rebuilt the steering box; (2) properly adjusted the mechanical brake linkage; (3) rebuilt your wheels (if required, which is by no means certain) and (4) put new tires on the wheels. As far as the engine, clutch and gearbox are concerned, the Chevrolet "Stovebolt 6" is an amazingly simple and robust unit, and was in production from the 20's until the 70's. Any shade tree mechanic can keep one going pretty much forever, with most parts available from places as diverse as PEP BOYS, J.C. Whitney, or any of the specialists who advertise in Hemmings Motor News.
My advice would be to sort out the car mechanically, slap on new tires, drive it about 100 miles per week, and at the end of a year think about restoring the body and interior.