Is it wrong to state that the thrust increases with time? Because it implies that it actually increases over increasing altitude, with time?
It strictly depends on the context.
Thrust increases with specific impulse, at sustained mass flow. Specific impulse increases with drop of atmospheric pressure. Atmospheric pressure drops with rising altitude. As rocket climbs, altitude increases over time. Thus, over that chain of dependencies, thrust of a climbing rocket indeed increases with time.
This effect is far less pronounced though, than increase of the acceleration caused by reduction of the mass of the rocket (by spending its fuel). And then we have thrust reduction around Max Q, where the engines are purposefully throttled down to reduce dynamic pressure impact on the rocket, and of course staging, where the upper stages will have fewer, or weaker engines than the launch stage, generating much less net thrust, but propelling much lower mass to both sustain reasonable acceleration (and g-loads) and not waste fuel on propelling empty tanks and unnecessary (any longer) engines.