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Examine the incoming Ampere waveform to get an idea what the emerging waveform looks like on your output resistor.

Even though you apply an initial square-ish Voltage waveform, the Ampere waveform is not identical. It's rounded. That initial Ampere waveform is similarly duplicated down the line from one LC stage to the next.

The first LC combination plays a key role in shaping the Ampere waveform. Smaller L causes quicker current ramp-up. Brief pulse causes less overshoot.

LC ratios do not have to be identical throughout. Even the simple Butterworth design uses different LC values in successive stages. A Bessel formula (mentioned in Tony's post #7) has LC values which are calculated to create a square-ish Ampere waveform.

Falstad's simulator menu has ready-made circuits which clarify these differences in filter types.