I put this heretical idea to Spencer White, a genial American boffin who runs a hi-tech laboratory in Boston peopled by jogging robots in Reeboks and professors from MIT. As Reebok's Director of Research Engineering, he warns that without decent trainers many of us who do aerobics, running or other sports would be hobbling around injured.
"Your foot bone is connected to your leg bone, and so on up the chain," he says. "Your foot is an extremely complicated mechanism, and if it's not a stable platform it can cause pain in the knee and as far as your lower back."
Proper footwear protects you from injuries such as planar fasciitis (sore heels caused by impact or not enough support) and shin splints (aches in the shins caused by lack of cushioning and stability).
Mr White's Human Performance Engineering Laboratory also has computer simulator machines which twist and bend and pound the latest Reebok prototypes in the new science of bio-engineering. Sometimes, real live athletes come to play basketball in the gym which is part of the laboratory, so that high-speed videos can record and monitor the performance of their shoes.
"There have been dramatic improvements in footwear for athletes over the last 20 years," says Spencer White. "But every foot is a different shape; every individual moves differently and has different needs." His aim was to make a running shoe which could supply all these needs, and with the new DMX Series 2000 he believes he has done it.
These trainers feel as light as a feather and look entirely synthetic, with semi-transparent blue soles rather like outsized bubble wrap. "This is the new underfoot cushioning and stabilising system," explains Mr White.
"It has been tested on more than 700 runners over thousands of miles and is better than and dramatically different from anything out there."
What is "out there" is already pretty sophisticated. Many of today's more expensive trainers have a "midsole" between the upper (toe box, heel box and fastenings) and "outside" or rubber bottom of the shoe. Midsoles are often made with air capsules, or gel using "energy return" chambers designed to cushion the shock generated when your foot hits the ground - which may otherwise travel up to your knees or lower back, with potentially painful results.
Some manufacturers use a shock-absorbent, spongy material in the midsole. Others use a hi-tech foam. Still others use adjoining chambers or a honeycomb effect so that shocks can be distributed along the shoe. But the bulgy outer sole of the DMX 2000 running shoe is, according to Reebok, a revolutionary development which they plan to adapt to other trainers in the future.
Its "active air transfer" sole has 10 hollow chambers connected by a network of channels that regulate the flow of air under your foot as you run. As your heel hits the ground the air is pushed forward, stiffening the sole to protect the foot from rolling inwards ("overpronation"). Then, as you move forward on to the ball of your foot, the air is forced back under the heel, absorbing the impact of the next step. It is a bouncy, rolling feeling as the air bubbles shift under your feet, but once you get your sea legs they are remarkably comfortable and springy, cushioning your feet as you run.Reebok clearly hope that the DMX 2000 will be the running shoe of the future, but the main consideration when choosing trainers is what you will be using them for.
"A serious runner needs a running shoe," says Mr White, "and if you do aerobics four or five times a week you will need an aerobics shoe. But if you run occasionally, but also play tennis, then a `cross-trainer' is the shoe for you." Cross-trainers should be light, comfortable and flexible with soles that will suit a range of surfaces, from modern gym floors to grass athletics tracks.
But do trainers need to cost an arm and a leg? "That cost depends on the quality of the materials and the research-and-development effort that went into them," says Spencer White - which perhaps explains why a pair of DMX 2000s will set you back pounds 110. The US annual spend on running shoes is $7bn (pounds 4.3bn) - equivalent to the cost of relieving the Third World's debt burden
So are we soon to face demands from teenagers to fork out huge sums for bulgy-soled trainers which they will grow out of - or wear out - within a few months?
It's true that children's feet are vulnerable while they are still growing, and if they are playing a lot of one sport - football, for instance - a good pair of the right (football) boots is the best protection.
But Spencer White has comforting words for parents caught in the battle of Which Trainers?
"For trainers that are mostly worn to school, and where there are no foot problems, the bigger issue is durability. You don't need to spend outrageous amounts of money."
The time to buy new trainers is when the cushioning of your old pair is worn out. Look from the back at the side of the shoe to see if it has become tilted. If in doubt take your old pair into a shop and try on a new one at the same time to compare how they feel.
Don't buy brand X just because you liked them last time. The technology of trainers moves fast: they could be very different this year.
Don't shop for trainers first thing in the morning. Wait until your feet have warmed up and expanded before you try on a new pair, or you may find they are too tight when you get into action.