Magnetic charge is in units of Webers, just as electric charge is in units of Coulombs. (This is all classical, pre-Einstein physics that depends on the idea of an aether and specialized constants describing that aether and Maxwell then presenting a case that these two things were related to each other, such that \$\mu_0\:\epsilon_0=\frac{1}{c^2}\$.)
Electric charge (Coulombs) divided by capacitance (Farads) yields the electro-motive force (Volts.) Magnetic charge (Webers) divided by inductance (Henries) yields the magneto-motive force (Amps.) That's the way things were seen. Bigger capacitors required less electro-motive force to store electric charge. Bigger inductors required less magneto-motive force to store magnetic charge. The key difference is that the electric force was imagined as volts and the magnetic force was imagined as amps.
Note that applying an electric force (Volts) for a period of time (seconds) yields a certain amount of magnetic charge (Webers or Volt-seconds.) Similarly, applying a magnetic force (Amps) for a period of time (seconds) yields a certain amount of electric charge (Coulombs or Amp-seconds.)
In this sense, a capacitor can accept an applied magnetic force (in amps), applied for a certain time (in seconds), and turn that into an electric force (in volts.) And an inductor can accept an applied electric force (in volts), applied for a certain time (in seconds), and turn that into a magnetic force (in amps.)
And now you might understand better what happens when you put a capacitor in parallel with an inductor. The electric charge of the capacitor is expressed as an electro-motive force on the inductor over a period of time, yielding an equivalent amount of magnetic charge on/in the inductor. This magnetic charge of the inductor is then expressed as a magneto-motive force on the capacitor over a period of time, yielding an equivalent amount of electric charge on the capacitor. And this repeats, assuming there are no energy losses.
To get to the meat of things, you can operate an inductor in any way you like, while keeping its constant of inductance, so long as you stay within its limits of magnetic charge (Webers) allowed by an inductor's design. This limit is controlled by the core material, where you must avoid exceeding its maximum accelerating Lorentz force (in Teslas, or Webers per meter squared.)
If you apply an electro-motive force (Volts) on an inductor for a certain period of time, that inductor will accumulate a certain amount of magnetic charge (Webers.) This "magnetic charge" is denoted by the number of amps flowing in the inductor (and the inductor's supposed constant value.) Similarly, if you apply a magneto-motive force (Amps) on a capacitor for a certain period of time, that capacitor will accumulate a certain amount of electric charge (Coulombs.) This "electric charge" is denoted by the number of volts on the capacitor (and the capacitor's supposed constant value.)
Just as you must discharge a capacitor, you must also discharge an inductor. You cannot keep building up magnetic charge on/in the inductor, forever. All that does is increase the current forever. You can increase the charge for a bit, then decrease it, then increase it, etc. Or you can start at zero, increase it for a time, then drop it back to zero. But there is always a maximum magnitude (plus or minus) beyond which you cannot go. Because the Lorentz forces acting in the core will eventually be too great.
Just think of the inductor like a capacitor and realize that you cannot exceed the charge limits allowed by the device design.
Of course, Spice doesn't care. As far as Spice is concerned, your inductor can tolerate any number of Amps without limit. Just as it also would allow a capacitor to tolerate any number of Volts without limit. You can get entirely aphysical results from Spice. You are supposed to know when you are doing something crazy. Spice doesn't care.
So of course current can just rise towards infinity in Spice. If you don't want that, then add mechanisms to limit the accumulation of magnetic charge in the inductor. Just like you would have to add mechanisms to limit the accumulation of electric charge on a capacitor. Similar idea.
Note: Magnetic force is actually a side-effect, because the effects due to the motion of charge take time to transmit across spacetime (speed of light.) Engineers still use the classical approach and treat magnetodynamics and electrodynamics as two different, but related forces. Engineers also still use Maxwell's classical approach which built on the idea of the aether and little tubular corpuscles (cells) that could be stretched or compressed. Einstein pretty much destroyed the idea of the aether and it's possible to reformulate Maxwell's equations in a relativistic form.
Best Answer
You should not use the startup option.
Do measure the voltage source V1 with this "startup" option and plot/see what happens to the voltage of the voltage source.
Use initial conditions instead, like
.ic i(L1)=0.