Is hand polishing effective?
It has to be noted that over the last 20 years, technology has changed, and the way cars are painted has changed, and car care products have adapted to meet the change. There was a time when cars were painted with a thick solid base coat which would be prone to fading and oxidation. Hand polishing your car every few weeks with a product like T-Cut Paint Restorer would do a fine job of removing the dead upper layer of paint using a combination of abrasives and chemicals.
Almost all vehicles are now painted with clear-over-base, fading is now seldom an issue and although your paint can still oxidize and require a hand polish, the effect or redox is far less noticeable. This is perhaps why products like AutoGlym's Super Resin Polish are so successful. This is a combination product which protects your car, applying a wax, but has a little bit of cut in it, so you remove that oxidation while you wax. Using a product like this will keep your car in great condition, without you having to polish, then wax your car, so you only have to do half the work. So in this respect, hand polishing your car is very effective and efficient.
However, this doesn't address the issue of scratches and wash marks. There are two real reasons for this, the first being that the cut in these polishes is very light, just aggressive enough to remove dead paint. The second is that when you are polishing by hand, you are not using a flat surface to polish with.
An analogy is that of using sandpaper. If you just use it with your hand, the sandpaper will form to the contours of whatever substrate you are sanding. It might take off some of the high-spots, but if you really want to sand something flat, you need to wrap the sandpaper around a sanding block.
With that said, hand polishing can be used to lessen the visibility of wash marks by rounding off the edges of light scratches. When a piece of grit scores a grove in your paintwork, it will leave sharp edges which catch the light, but polishing it, even if you don't cut the paintwork back beyond the scratch, those edges get softened, and that will soften the reflected light. In combination with a wax which is advertised "ideal for dark coloured cars", which generally means it's designed to hide scratches with fillers and diffusers, you can really improve the appearance of your car.
If you really want to be rid of all those wash marks, machine polishing is the only effective way.