Well, yes but no.

Boiling water is not by itself an issue as demonstrated by the very satisfactory operating record of BWR reactors in the US and Western Europe. The idea of using the primary coolant to directly spin the alternators is a bit freaky at first look but, in practice it works well, with the added benefit that it induces very rigorous safety practices.

The issue is that the RBMK design is a dual-use reactor. Producing power is one of its goals but the most important goal is to produce weapon-grade plutonium. Even if it was outwardly a civilian operation, Chernobyl is, like every real nuclear disaster, deeply related to military use of nuclear energy.

Every single flawed design choices made in RBMK derives from that breeding capacity. At the top of the list comes the choice of graphite moderation with ordinary water coolant. With this design, the ordinary water that flows along the fuel assemblies and vaporizes plays the role of a neutron absorber, not that of a moderator as in PWRs or BWRs. It means that to compensate neutron loss in the coolant, the design must have higher reactivity than it would need to maintain criticality if the reactor was dry. So, if too much coolant vaporizes (excess power), less neutrons are absorbed by that missing water and those excess neutrons reach the graphite moderator, get moderated and reach fuel assemblies to create more reactions. The power of the reactor goes up and so on.

I believe (not 100% sure) that under normal operation of a RBMK, the stabilizing effect to excess power is that if there is a localized hot spot, the pressure tubes around the hot spot generate too much steam (bad) but also make the pressure rises in the whole reactor, bringing more water back in dense liquid phase over the whole core so more neutrons are absorbed and overall power goes down (good).

But, in the case of a large, sudden breach in a pressure tube, the reactor goes dry with excess reactivity and a reaction runaway is guaranteed. And at Chernobyl, the whole pressure system ruptured at once with the power spike. The same effect, that ordinary water is not a moderator but an absorber in this type of reactor, also explains the role of the graphite tips on the control rods in the lead up to the power spike.

Mixing graphite and water is simply evil. Note that the US military program used uncomfortably similar systems for weapon-grade plutonium production at the Hanford site. All reactors were closed between 1964 and 1971 except for one, Hanford-N, which, interestingly enough was also a dual-use plutonium/power reactor. It was closed in January 1987...

I did not mentioned Doppler broadening as a safety feature in PWRs and BWRs because, as you mentioned, it plays a role in driving the reactor, but it plays no significant role in a catastrophic LOCA situation.

The big last line of defense when a PWR or BWR suffers a massive loss of coolant (like at Three Miles Island) is that the coolant is also the moderator. If the cooling water evaporates out of the core, the neutrons are not moderated anymore. They leak outside of the active core area without having the time to reach levels of energy low enough to sustain the fission reaction while in the core. The reaction stops and the only remaining power output in the core is the residual decay heat from short-lived fission products, about 10% of the operating power. TMI was bad but did not come anywhere close to Chernobyl in good part for this reason. The core slowly self-destroyed but could not really explode.

This mechanism also plays a role in the normal operation of BWRs. The reactor are protected against vaporization instability because too much steam in the core reduces moderation and, as a consequence, it reduces the reactivity, hence the power output. Nice negative feedback.

PS: You like PBRs ? Personally, I'm not convinced ...