You want to multiply [$]\sigma(t)[$] with a mixture of a constant and [$]L(t)[$] to produce something between a flat smile and a skew. Since the scale does not matter, [$]\alpha L(0) + (1-\alpha) L(t)[$] is a clever choice because this factor is always in the order of magnitude of the Libor rate itself and [$]\sigma(t)[$] stays therefore always at the same level too, which is good for calibration, since [$]\alpha[$] and [$]\sigma[$] are not interacting, but are "orthogonal". You can also take [$]L(t)+d[$] for example, but then [$]\sigma[$] varies between a normal volatility if [$]d\approx 0[$], i.e. something like [$]0.0050[$] for example and a lognormal volaility if [$]d\approx 1[$], so something like [$]0.30[$]. That's not nice for calibration obviously.