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In my opinion, respecting what the HR diagram tells us on the evolution of the star is quite imporant. It would greatly improve the consistency of the SE universe.
It would indeed, but there are several reasons why this is currently an outstanding scientific endevour. It would result in publishable papers and not only on SE improving its quality. Let me explain why this is so complicated with the example of ESA's Gaia mission.
Gaia has catalogued almost 2 billion stars by now. The result of this mission include distance estimates for more than 1.5 billion of them, and thus are potentially the future of the non-procedural part of SE in the Galaxy. We only need to know their classification and we will have enough information to have them inside SE with more or less consistent and realistic parameters. But for that the best thing is to gather their spectra. But we can't. Why? Taking spectra requires time, you need lots of photons so you can sort them out in terms of their colour, and have enough photons in each slot of the spectrum for a consistent signal. Gaia has the largest catalog of stars but it has it because it spends very little time observing each one (in fact it observes around 460 stars each single second). A modern telescope could gather spectral data for a star within minutes but if you do that you have to sacrifice the numbers since it would take thousands of years to gather a similar number of detections as Gaia. Currently there are almost a million times less spectra than stars are known, and this can hardly improve significantly for the moment.
But hey, maybe we don't need the entire spectra to classify a star, maybe we can make it only by using photometry (which Gaia has). We could use an HR diagram to discriminate between different populations, as you said. That seems fairly good in theory, but in practice it is not. Take for example OB stars; you have stars that look red and still are blue massive stars, but they look red because they generally are far away and interstellar dust filters their blue colors (it is difficult to tell the difference between a nearby small hot star like sub-dwarfs and a massive Ob star and a red supergiant not as far). In theory distance estimates should make this easier to disentangle (but distance estimates are not accurate enough for large distances and interstellar dust can present overdensity fluctuations across the sky that make the effort really unworthy). So in general we are unable to distinguish OB stars from some red supergiants. To accomplish that we need very accurate extinction laws (rules that tell us how the different frequencies of light are attenuated by the Galactic dust), but we currently lack any extinction laws that might be good enough for this goal. We still have huge unknowns in terms of what properties the dust has (grain size, different chemical mixtures and proportions, and density at every distance and direction in the sky). Worst of all, our knowledge on the galactic extinction laws is built by measuring the spectra of stars and reconstructing how the dust in the line of sight has changed that spectral footprint, by knowing before hand about stars with similar spectral features that are nearby, so we end up needing lots of spectra all over again, to solve the main problem.
If we knew the exact form of the Galactic extinction laws (or at least with enough accuracy), we could reconstruct the real position of the vast majority of stars in the Gaia HR diagram as they would appear if no extinction was involved. Then we could apply some classification criteria. But for now this is impossible for the vast majority of stars. Also notice that there are more stars farther than closer (following the square-law), because "closer to you" is a much smaller volume of space than "farther from you", this means that the majority of stars are behind some non-negligible level of interstellar dust extinction and thus photometry really needs to be accompanied by accurate Galactic extinction laws, to allow for classification.
And if that weren't enough, there are other issues. For example, stars with discs around them are reddened (because of the visible tail of the infrared emission), that is the case for Be stars for example, which means you would classify them wrongly. We are also not considering the problems related to binary systems. Some stars that Hipparcos includes are not single but binaries that weren't separated at the time. If you have a blue star and a red star in a binary system that you can't separate with Gaia or any telescope and rely only on photometry, you would think you are dealing with a single star with a classification that doesn't match either of the two components whatsoever. The HR diagram can't help you on this, and a lot of work has to be done first to discover what are the binaries. After you discover what are the unresolved binaries of Gaia (which is a huge scientific task on its own), you can do two things; either you ignore all those cases (but they are probably something like 30% to 40% of the sample considering how common binaries are) or you take spectra of the system and separate the two spectra by doppler shifts between the lines of one component and the other (something that relies on spectra again and on the convenience of the orbits of the system being not perpendicular to the line of sight).
In the end is a very complicated issue. It would be solved if we had spectra for all the stars, but we currently don't have telescopes with enough aperture to gather so much photons as quickly as needed to generate high-resolution spectra of each and every star of the large catalogs in a human lifetime. We also don't have the angular resolution needed to separate the huge amounts of binary systems that might escape us right now. But one day we might have that, and when we reach that goal, we won't only have the stars correctly classified but also chemical footprints particular of each one of these stars, their ages, and much much more.
What you currently see for Hipparcos en SE is the best we can do with Hipparcos. In general they are more or less accurate but you will find lots that are not, and if there are not specific scientific articles taking spectra for specific stars you won't have any basis to change the way it is. We can only improve one by one right now. Since that is impossible with the 2 billion Gaia stars we really need some automated way of dealing with it. Until then you have to know that HR diagrams are not the solution.