I'm not sure that there needs to be any more profound answer to this question than "tradition." Once someone does something in politics in a particular way, others tend to follow that precedent without a good reason to do otherwise.
Having a top communist party official who did not hold governmental office worked for early communist leaders in Vietnam (and honestly, there haven't been all that many so this is really just the decision of a dozen individuals, only seven of whom have served in the top party position since the single party regime in Vietnam was established), and so those who followed did the same.
As noted in the comments, both Stalin and Brezhnev were precedents for having a communist party leader who did not hold a governmental office in the USSR's regime that was a model for the regime in Vietnam. And, by the end of Brezhnev's rule in 1982, after which later Soviet leaders decided to hold state positions as well, Vietnam had already started to develop its own traditions and political precedents. The fact that the Communist Party in Vietnam expressly conceptualized itself as Stalinist rather than merely Communist, probably made the example of Stalin who ruled the USSR without holding a governmental office for many years, particularly salient.
And, of course, as the examples of the USSR and Vietnam demonstrate, it is perfectly feasible in a single party state for a party leader to run the country from behind the scenes without actually holding a governmental office. Further, this arrangement frees the party leader to focus on policy and political priorities without being burdened by the day to day tedium and inconveniences and responsibilities of a governmental official (and equally important without the transparency that a governmental official must have in terms of following formal and usually public processes).
The party leader is not normatively pressured to attend state dinners and funerals of VIPs, and dedications of new public buildings, etc. if the party leader doesn't want to, while a head of state would be expected to do such things.