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The problem isn't frequency per se. Granted, frequency (actually pulse width) has a lot to do with the energy deposition amplitude in pulsed systems, but it isn't a matter of finding the right frequency, it is a matter of having enough joules in a single pulse.
A better way to explain it is this; pulsing a CW laser does not a "pulse laser" make. In other words you can pulse your 5W 450nm diode as fast as you want, but it will NEVER cause induced air ionization.
There are a few ways to generate laser induced plasma breakdown of air, all of them involve Q switched lasers. The typical lasers are Nd:YAG (pure (IR), doubled (532), tripled (355), and quadrupled (266)), CO2, N2 (not TEA), Ti-Saph, and Ruby. These lasers deliver many joules of energy per pulse. If these were to operate CW or QCW you'd be talking about kilowatts of power. Handheld technology cannot even store enough pump energy to power one of these lasers. We can get close with Nd:YAG by using a backpack based power and cooling system, but it would be an engineering feat.
An important thing to note is that these lasers do not induce a plasma channel the entire length of the beam, but only at a single focal point where the laser is focused.
Mechanics: air ionization (of a theoretical source, not from laser light) would result in a plasma channel forming along the axis of ionization not perpendicular to it. In other words if you have two plasma-inducing-fictional-laser beams facing vertically with a distance between the two parallel beams and placed an electrode at each beam's ionization spot nothing would happen (other than two loud bangs). No current would flow as electrically it is the same thing as having slightly longer electrodes. There is no path for the current to flow since the ionization points are parallel and the voltage isn't enough to break down the gap between points. If you have the two points on lines that intersect at some point then you could have a current flow provided the charge voltage is set so that it doesn't break down the gap until the gap is slightly shortened by the ionization of the focal point.
It wouldn't be a continuous flow though, it would just be a momentary pulse of electricity. High current discharge would allow for thermal energy from the discharge to extend the life of the plasma, but only for a short period before convection kicks in. Convection draws the ionized air up and out of the plasma channel, and nonionized air replaces it from below. This regular air presents a higher resistance, which restricts current, increases the voltage drop across the arc, and soon the arc extinguishes. You wouldn't get a traveling arc as in a jacob's ladder, as the ladder electrodes form a new jumping off point for the vertically rising stream of ionized air. If you film a ladder in high speed it is actually a series of individual air breakdowns that follows the initially ionized air upward. Also, the voltage has to exceed the air breakdown potential of nonionized air to initiate the process. In the laser induced ionization example the voltage is less than the nonionized breakdown potential so after the ionized air moves upward and the arc extinguishes there is nothing left to initiate another arc. You could use another pulse from the laser but there's not much point, raising the voltage would allow repeated arc formations without the need of expensive, fragile, and overly complex laser systems.
