On the one hand, China would have the resources to make a far more ambitious showing in space, if they really wanted to. They could easily outpace the early space-age Soviet launch rate etc; this would make a vivid statement about their prowess as a nation, but it wouldn't really do much more than that (until they get to the point of, I don't know, mining asteroids or something).
On the other hand, they could equally take the view that human spaceflight is totally frivolous and they should keep their investments firmly rooted on Earth. This would be hugely short-sighted -- abdicating the rest of the universe to whomever has more vision than them. In fact, China did this already, when they reined in Zheng He, burned the Treasure Fleet, and focused all investment inward. The result was centuries of humiliation, which China is not particularly keen to repeat.
So the path that they're taking seems to be keeping one foot prudently planted in space, without going nuts. When it's strategically important to make a major push in space, they'll have the technology and the experience to do that. Until then, they've mostly got other fish to fry. It seems to be a pretty reasonable approach.
The US went from its first suborbital spaceflight to landing two people on the moon in just over eight years. But that furious pace didn't really work out very well in the long term. Maybe they mean it but are just taking their sweet time.
Whilst it might be valid that you could launch a more-effective-in-aggregate fleet of rovers for the cost of a manned mission, I'm still a huge proponent of getting people out there to have a look around.
In addition to that however, sending a human crew to Mars will result in more digging, surveying, water prospecting and life hunting being done within the first month of exploration than all of the rover missions combined.
The added benefit of having humans in space, especially if their reason for being in there is because that particular bit of space is in the way of earth and a planet, is securing the legacy of the human race by putting our eggs in more than one basket.
To that end, I'll flip your assertion back on you: The only reason to send a robot to space is to prove that you can, especially if we don't follow it up with human missions.
Remember, this isn't just wishful thinking. We can do a side-by-side comparison:
The Russian Lunokhod Moon rovers were engineering marvels, vastly outperforming most of NASA's Mars rovers… and they're barely worth a footnote in our exploration history of the Moon, because Apollo astronauts collected more data during lunch breaks than the Lunokhods in a good week.
And the US hasn't done a manned flight since 2011, so China a doing great comparatively!