This was kind of true early on, and got less true both as the size of the nobility grew (especially in countries like France and Russia, which had serious nobility surpluses) and as a professional class of government emerged (by the time you get to Samuel Pepys, you're talking about largely a professional government). Even before that in practice many or most government functions were carried out by appointed or elected commoners.
To take a ridiculously over the top example, take the samurai class in the Tokugawa Shogunate. They were about 10% of the population, and by and large weren't really allowed do anything much at all (beyond wars, but there were no significant wars during that period). 99% of them were pure drain on the economy.
> as well as the investor class
This is way more dubious. Obviously it depends on the time and place, but in most times and most places it was anything from socially unacceptable (England) to effectively illegal (Roman Republic/Empire) for aristocratic landowners to invest in non-land things. What little investment in productive projects there was was largely by merchants, money lenders, and later banks, all generally commoners.
can you expand on this? It's harder to think about "investment" opportunities back then because the economy was basically agriculture, the slave trade, urban real estate, and trading the fruits of agriculture and slavery. I think landowners in the Roman Empire did in fact partake in other business, say starting gladiator companies.
I think it somewhat depends on the era, but in general if you were a senatorial family, you wouldn't want to do this, because you'd lose your senate seat (and might face other sanctions from the Censor). There were rich non-senatorial-class people, some of whom would have been much richer than most of the senators who might own land along with other stuff, but the big landowners were generally the senators, because they weren't allowed do much else. I think even, say, building an apartment block on land they owned was dubious territory for a senator. Mercantile activities were right out.
In the English case, the landowning classes generally didn't invest in non-land things, and arguably the trigger of the industrial revolution was less the technological advances, and more the development of the capital infrastructure to invest in using them (banks, joint stock companies, etc).
In the middle ages the nobility were effectively the government (and the church provided checks and balances, kind of) as well as the investor class. In addition to financing productive capacity they also did all the administrative things governments do. Obviously administrative bloat ebbed and flowed over time. Today we have both government investment in capital project (e.g. a road, or a bus terminal) and private investment in capital projects (a new factory or whatever). Both groups can get very rent-seeky and non-productive if left alone with no reason to not do those things. It's really hard to make generalizations that are more accurate than not.
I think comparison to the pre-industrial world is more effective for understanding that time than it is for drawing conclusions about our own time. All the details are so different you really need to squint to make things line up and when you're talking about big things like macro-economics it's the fine tuning and details that make all the difference.