It’s safe to say that most tube amps that are considered to sound good cost at least $2k. We know that correlation doesn’t imply causation, so let’s try to unpack that (also see @Jsim’s comments above).
There are some poor performing amps that cost more than $2k.
Factors that may contribute to a sub $2k amp performing well despite being in no man’s land: DIY and thus less labor cost such as Bottlehead; cheaper cost of production outside of the US such as in Russia with the SW51+; OTL/hybrid/parafeed designs that don’t require the cost of expensive output transformers such as LTA/CSP3/Tuba/Lyr 3.
LTA and Decware focus on stereo where many of their products cost significantly higher than $2k. Some of the technology/R&D/know-how/processes present in their higher priced gear likely trickles down to their sub $2k gear, as opposed to a manufacturer whose $1500 tube amp is their most sophisticated and advanced offering. The base MZ2 and CSP3 priced at $1300 can be configured with upgrades and a total cost up to $3k.
Perhaps the sub $2k no man’s land guideline that seems to have originated in a prior year should be refreshed (or eventually and not considered fixed) or qualified to refer to transformer coupled tube amps - - for inflation, technology and innovation should improve over time for producers to be able to make equivalent quality products for less cost, change in cost/access to raw materials including stock tubes. Or maybe it doesn’t need to be refreshed and we declare the price of the Starlett, Pendant, T4 as the minimum entry point. Or maybe one has a preference for transformer coupled sonics (associated distortion) over OTL sonics, making the price of OTL amps irrelevant.
A fair fight might be to compare tube amps with similar caliber tube complements, which might mean upgrading the stock tubes in cases where the manufacturer skimps. Yes, an amp should perform adequately in its stock form, but here the objective is optimized sonics and declaring an absolute no man’s land.
That being said, advising $2k as a minimum is a helpful guideline and makes it very likely that one will end up with good tube sound, but should be put in context and perhaps is not an absolute. Maybe it’s all relative. Such no man’s land characterizations, while generally true, are on par with “if you ain’t listening to directly heated triodes, you ain’t listening.”