It's pretty simple. Think about those kiddy shoes that have blinking LEDs. Most of those are powered by the energy of walking. (There are some that use battery but most are piezoelectric). The kids that wear them don't fall over, even when climbing a hill.
You assume that to generate storable energy, 1) extra energy will have to be generated and 2) walker won't be able to compensate for it. Both assumptions are wrong. Firstly, the energy used to charge the device can be deducted from the proportion dissipated as heat (making walking technically more efficient) without requiring additional energy. Secondly, if efficiency is not increased, it is possible for walker to adjust output to compensate, rather than to fall over. Not any different than walking up a hill unloaded, and then walking up the same hill with a 30 lb. pack on. The centre of gravity is different with pack, the walker uses more energy, but does not become unstable and fall over as per your somewhat ridiculous assertion.