Inaccuracy and mismatch of integrals in LTspice
Setup

According to the comments from PlasmaHH, a concerned citizen and my assumptions there are several possible error sources. Therefore I modified the SPICE simulation to do parameter sweeps over frequency and amplitude of the sine wave, as can be seen in the next figure. Additionally maximum timestep and numdgt were adjusted manually.


The image shows a normal voltage source V1 set to produce a sine wave. The last set used such a source, while the other two sets used an arbitrary voltage source as in the question. 

Results
Setting a smaller maximum timestep reduced the Error of the energy tracking arbitrary voltage source (Error E_a) to negligble values, when tracking an arbitrary source. The error from calculating the energy directly (Error E_t) was reduced as well, but was still significant at 10 kHz when using a maximum timestep of 10 µs.
The differences between numdgt = 15 and numdgt = 6 have no impact on the error down to 0.01 %. 
Using a normal voltage source V1 reduces the error of outliers (e.g. at 10 kHz), while it elsewise decreases the accuracy of the tracking arbitrary voltage source.

Conclusion
For the given circuit tracking the power of the source with an arbitrary voltage source at 10 µs or faster leads to a good compromise in accuracy and speed.
When calculating the energy directly (.meas E INTEG V*I), a fine maximum timestep has to be used, in this case 2 µs. 

Data
The full results follow here: