Mysterious energy disappearance of capacitors
The simple answer is that you cannot short circuit two ideal voltage sources without creating an over determined system of equations. So if you try to use network theory to describe the circuit you have drawn, it will always fail. As others have pointed out, to make this circuit calculatable, you need to add some parasitic component (parasitic resistance would be easiest to model and understand).
When we try to work with Kirchhoffs laws, there are two equations for the voltage over your capacitor (like you drew it).
$$
v_C(t) = V_{bat} \quad; (1) \\
v_C(t) = V_C(0) + \frac{1}{C} \int i(t) \mathrm{d}t \quad; (2)
$$
(1) Follows from KVL because the battery is also a voltage source
(2) Because of the definition of voltage on a capacitance
Obviously, they can't both be true if there is any current flowing in the circuit. This is why any mathematical approach to describing your system without extra parasitics will fail.
There is an easy, non-mathematical explanation to why no source without parasitic resistance can exist in reality: Having a voltage source without internal resistance means that this source will deliver any current at its fixed voltage. This means that the source would be able to provide any or infinite power, which can't be true in a physical system.
Because of discussion in the comments:
Kirchhoffs laws are not some kind of mathematical super tool that apply to anything and everything you can think of. They laws can be understood as a special case of Maxwells equations for low frequencies. We believe that Maxwells equations are the best description of electromagnetic phenomena that we can work with (maybe some kind of quantum theory will supersede it one day). And even with Maxwells equations you couldn't find a consistent description of your ideal lumped circuit. You cannot use equations that describe reality and try to apply them to something made up.

What exactly is wrong in this derivation for k.v.l ( The Feynman Lectures on Physics, Volume II, Chapter 22: AC Circuits)
∇×E=−∂B∂t=0

In an earlier version, I tried to show some contradictions in Maxwells equations when applied to your circuit. This explanation was flawed because when transitioning to Maxwells equations to explain what's going on, we have to assume that there exists an inductance in the circuit. So already at this point, I was deviating from the actual lumped element model of your circuit, as Sredni Vashtar has pointed out.
This is because of Amperes law, one of the Maxwell equations:
$$
\nabla \times \vec{H} = \vec{J}
$$
This states that any current density is always linked to a magnetic field. Since inductance is a measure of how much flux a circuit produces per current, it can not be zero in reality. This also leads back to the explanation, that your lumped element model cannot be a description of a real thing.