  Reading out the state of superconducting artificial atoms typically relies on
dispersive coupling to a readout resonator. For a given system noise
temperature, increasing the circulating photon number $\bar{n}$ in the
resonator enables a shorter measurement time and is therefore expected to
reduce readout errors caused by spontaneous atom transitions. However,
increasing $\bar{n}$ is generally observed to also increase these transition
rates. Here we present a fluxonium artificial atom in which we measure an
overall flat dependence of the transition rates between its first two states as
a function of $\bar{n}$, up to $\bar{n}\approx200$. Despite the fact that we
observe the expected decrease of the dispersive shift with increasing readout
power, the signal-to-noise ratio continuously improves with increasing
$\bar{n}$. Even without the use of a parametric amplifier, at $\bar{n}=74$, we
measure fidelities of 99% and 93% for feedback-assisted ground and excited
state preparation, respectively.
