Everything has resistance and here it is relevant.
The maximum current thru the Inductor must not exceed the Absolute Maximum Rating of the LED, otherwise, MTBF degrades rapidly. (even instantly)
What limits the current?
The battery has an effective series resistance ESR like e-caps measured by a short pulse low R shunt. (don't blow your DMM fuse) This is predictable for many chemistry types.
The inductor has a low DCR and will be very low for 1uH.
An LED will have an ESR or Rs bulk resistance inversely proportional to its power rating and somewhat with voltage. e.g. 5mm Red is ~ 10 Ohms, 5mm White is 15 Ohms at rated current. This rises exponentially at low voltage and also has some capacitance.
What limits the rise time and fall time?
\$V=L ~ dI/dt\$
Although this circuit when switched rapidly can boost voltage to create a steady DC to drive an LED it must be pulsed to perform as an unregulated switch mode supply.
The energy stored depends on E=0.5 L I^2 in Watt-sec [J] but the self-charge time constant depends on the L/R for series current.
So it is possible to blow the LED with excess current using a manual switch.
In order to raise R and L for longer visible manual operations and thus limit current for short momentary contacts, consider the example below and compute \$T_{\text{63%}}=L/R\$ and \$dI/dt= V/L\$ using the plots.

The LED leakage current of typ. 1~10 uA is modelled with a shunt R.
Also, most switches have contact bounce and depends on spring force and power rating. Typ 1 to 15 ms.