Initial current value in capacitor charging circuit
While the first diagram is pretty and simple, it's too simple to be worth simulating or drawing a graph for the theoretical current. It never occurs. It is a picture of a switch with zero resistance, connecting components with zero resistance. The initial current will therefore be infinite, which is non-physical. Think of it as that hoary old puzzle, an irresistable force pushing an immovable object. Given the terms as presented, it's not analysable.

The graph they present shows a decay to the current over time, which implies some resistance, contrary to the diagram. They say 'high losses', but where is the dissipative component? There is no resistor shown. When we draw schematics, all components are assumed to be ideal, a capacitor with no ESR, a battery, switch, and wires with zero internal resistance.

The second diagram rolls up the series resistance of the switch, the power source and the capacitor into one R, which then controls the initial current. For small R the initial current will be large. For large R, the initial current will be small.

Interestingly, for the same capacitor and voltage, the losses are independent of the value of R, once the capacitor has become fully charged. Although in theory, the capacitor never becomes 'fully' charged, in practice, the error becomes exponentially smaller over time, and after 5 or 10 RC time constants (depending on your need for accuracy) it is generally considered to be fully charged.