The MLZ series of inductors is not designed for power conversion (buck, boost, etc.), but instead for power supply filtering. This means that a) the windings are not optimized for low skin losses, and b) the magnetic core is not optimized for low core loss. From a circuit design perspective, this means the boost regulator will be less efficient.
If efficiency is not what you're after -- if you simply care for functionality and compactness -- then I don't see any problem using MLZ (or other "ferrite choke") inductors, as long as your circuit doesn't overheat. In practice, this means sticking to low power levels. Just ensure the current rating covers your needs (with healthy margin), and evaluate the power supply thoroughly.
For the circuit you have drawn, yes, the voltage spike has nothing to do with the value of the inductor. It is given entirely by the value of the current in the inductor, and the resistive load R2 across it.
What does that mean if R2 is a higher value, or even absent? In theory, with what you have drawn, if R2 was open circuit, then the voltage spike would be infinite. As you can guess, that doesn't happen in real life.
In practice, there are two things omitted from your drawing.
a) the stray capacitance across the inductor, and due to any wires from the inductor terminal to ground
b) any breakdown mechanism for your switch
capacitance
As the switch opens, the current will start to charge the stray capacitance, which will limit the rate of rise of the voltage. For large value inductors, with many turns in close proximity, this capacitance can be surprisingly large.
Sometimes an external capacitor is added to the inductor deliberately to reduce the rate of voltage rise.
No matter whether your switch is mechanical one with opening contacts, or a semi-conductor one like a MOSFET, it will not support an infinite voltage.
the switch
Mechanical switches are especially poor at breaking the current flow, as at the first break, the contact separation is very small, and an arc needs very little voltage to form. This arc will keep the current flowing, and damage the contacts. It is responsible for switch and relay failure, unless controlled.
In the old-style contact breaker car ignition system, the 'points' that connected and disconnected the coil to the battery could be subject to excess erosion from arcing. Often, the first sign that your 'condenser' (capacitor) had failed would be excessive wear at the points. The capacitor, fitted across the points, slows the rate of voltage rise so that the points are sufficiently far apart before the voltage gets high enough to create an arc.
The specifications for a MOSFET will typically give a breakdown voltage figure. Good ones will also give an energy they can withstand when the breakdown voltage is exceeded. As long as the stored energy in the inductor is less than that figure, a MOSFET can switch current off to a coil, limit the open circuit voltage to its breakdown voltage figure, and survive.
Best Answer
Unfortunately you are talking about many different types of inrush, all caused differently, so with different cures. Some 'caused' by inductors, some cured.
a) Motor inrush
Motors generate a back EMF when turning, and this cancels out most of the input voltage, leaving only a small net voltage to drive a current through the small motor resistance.
At standstill, there is no back EMF, so the normal supply voltage may drive typically 10x the rated current into the motor. The motor inductance is insignificant compared to the mechanical time constant of the motor. It's enough to level out PWM switching in the many kHz range, but not to cope with the seconds of acceleration.
Small motors just live with the inrush. Bigger motors need to use some form of controlled gentle starting.
b) Transformer inrush
Flux can be measured in volts.seconds. A transformer core has a maximum flux. It is designed to swing from -max to +max and back again. The transformer has zero flux before switch on. If you switch it on at the wrong part of the mains cycle, then instead of swinging between -max and +max, it will try to swing between 0 and +2max, which is obviously not possible. The large assymetrical current drawn due to saturation causes a net DC voltage in the winding resistance, which gradually shifts the flux to zero average over the next few cycles.
While some people say this is 'caused' by the transformer inductance, it is actually because the inductance falls when the core is saturated. This is generally mitigated by using a time delay fuse, that will stand the extra current for a second or so.
c) AC solenoid inrush
When a solenoid is un-energised, there is a large air-gap in the magnetic path, which means the inductance of the solenoid is low. When AC power is applied, typically the resistance of the coil will dominate, and a large current will flow. When the solenoid closes, the air-gap disappears, and the inductance increases by an order of magnitude or two.
In a well-designed AC solenoid, the inductive reactance will now dominate the solenoid impedance, causing the supply current to fall significantly. This fall in current happens automatically as a result of the changing magnetic circuit geometry.
d) DC solenoid, no inrush
As the supply is DC, the steady state current will be limited by the resistance of the coil, not by the inductance, whether large or small. The inductance will serve to slow the increase of current, the opposite of an inrush.
When energised, the smaller air-gap means less current is needed to supply the holding magnetic field. A special driver is sometimes used to supply a large pull-in current, which is then reduced to a lower hold-in current. This is done actively by the driver, not as a result of the solenoid's changing geometry.
e) Rectifier/capacitor switch-on inrush
In the first cycle, the supply has to charge the capacitors from zero. This can be handled by using a time delay fuse, and surge-rated diodes. The ubiquitous 1N540x series for instance are rated at 3A continuous, 200A half-cycle surge. Another way is to use NTC thermistors in series, or relay-shorted starting resistors. It's not practical to use a large enough inductance to limit the rate of current rise.
f) Rectifier/capacitor recharge inrush
Now this one can be mitigated by extra inductance. The capacitors are charged only when the input voltage exceeds the capacitor voltage, which might only be 10% of the time. This leads to a very peaky diode current waveform. A bit of series inductance, sometimes a discrete inductor, sometimes the transformer is wound to have finite leakage inductance rather than the minimum possible, will extend the current pulse. As the pulse starts, it limits the rate of rise. When the transformer voltage falls and the pulse would normally end, the back emf in the inductance adds to transformer voltage, keeping the pulse going while the pulse current drops to zero.
g) Filament lamp inrush
The resistance of a metal filament changes by more than an order of magnitude form cold to hot, so at switch-on, the current can be 10x the running current. This is handled with over design, or time delay fuses.