In general, the number of shots does not increase the accuracy of an experiment. Rather it gives a more precise answer. Attached is a figure showing the distance (in terms of Hellinger distance) for a Bell state run on the IBM Quantum Boeblingen device from the theoretical answer as a function of the number of shots taken. For each value of the shots, the experiment is repeated 100 times.
We see that as the number of shots is increased, the spread of the distributions decreases, following a $1/\sqrt{\rm{shots}}$ scaling. Therefore our answers are becoming more precise. However, the mean of this distribution is fairly constant, and it is clear that it converges to a nonzero answer, $\sim 0.17$ in this case. Ideally this should converge to zero distance, and the difference is the accuracy of the experiment. No matter how many shots one takes, this accuracy does not improve. This is because of errors in the device such as gate errors, measurement errors, environmental noise, etc. In this particular case the dominate error is measurement error that can fortunately be mitigated.