That is what they are doing from the look of the design, optimizing for mission. But I don't see it a mistake. It can not be wrong if that is what people want.
But it is a mistake to say that their design is focused on moon mission. CZ-5DY's single core configuration is certainly meant for near earth crew mission.
I have nothing against optimizing it for the mission if it still allows for reusability to be developed in subsequent variants.
But I think if strategic decisions for rocket development have already been made which does not emphasize reusable heavy and super heavy lift rockets (either as iterations of in development designs or new designs yet to be announced), then I think that their priorities are heavily misplaced, potentially fatal.
Reusability is good, but there can be more than one approaches than SpaceX's "all in one" solution. China seems to be going for two categories of rockets 1 mission focused 2 general purpose reusable. I don't see why what SpaceX has been doing is the best approach for China. After all, SpaceX's scope is not the full scope of US space ambition and it can not be compared with China.
I remain sceptical of Starship. Technically it is just another rehashed Space shuttle sacrificing the flying ability for the increased payload (which has shrunken to half of its promise). It's elastic shrinking ambition of performance isn't impressive at all. So I don't see there is a gap.
My view it has to do with priority.
In the last few years, I think it should have become somewhat apparent that being able to carry out a large number of launches of relatively large payloads into earth orbit is much more important from a geopolitical perspective than being able to conduct the perfect moon or mars mission.
The idea of pursuing separate rocket categories -- one mission focused, and one general purpose reusable -- would be ideal if they had the money, time and resources for it.
After all, the pursuit of reusable rockets in the medium and long term is to consistently and regularly launch over 100 tons of singular payload into earth orbit in a single rocket launch, which would naturally require a very large reusable rocket (CZ-9 class) to do.
Given that, I don't see what the purpose of "mission focused" and "reusable" categories would be once you get to that size -- even if you had the money, time and resources to fund both options, wouldn't the much lower costs of a "reusable" superheavy launcher be able to offer similar mission performance to a "mission focused" launcher if they simply launched more of the "reusable" rocket?
E.g.: if a launch of a "reusable" super heavy is 1/3 the cost of a "mission focused" launch, even if the "reusable" rocket only had 60% the effective payload of the "mission focused" launch, you can still carry out three of those 60% payloads at the same cost.
Or putting it another way -- before there was an estimate from CASC that China would require 10 CZ-9 rockets between 2030 and 2035 (i.e.: two launches a year). There was some confusing phrasing there, as at the time some places incorrectly translated it as "10 CZ-9 rockets per year".
But I think even 10 CZ-9s per year may be potentially dangerously low, and
10 CZ-9s per week may be needed to keep up with the launch pace that the US would likely be bringing online by that time.
The most dangerous scenario is if a nation is able to monopolize large scale orbital launches while the rest of the world has to contend with smaller payload launches. E.g.: if a nation is able to annually launch the full displacement tonnage of a super carrier (100,000 tons) into orbit every year, while others can individually manage a couple of hundred tons per year.
As to starship, in terms of the capability offered, I was more thinking about the reusable first stage "Super Heavy". The actual Starship spacecraft itself is somewhat less important. The reusable "Super Heavy" first stage is what will enable the US and SpaceX to develop more conventional second stages that will be able to put 100 ton class payloads into orbit in a reusable fashion.