Apologies for the lecture....
The daughter products can (in quite a few cases) act as neutron absorbers - Xenon in probably the worst (but is very short lived - it can pose a significant challenge to reactor management when output levels are being adjusted, imposing a limit on how fast power can be ramped-up). That's unrelated to heat production. That cuts down the total amount of neutrons available to maintain the chain reaction (I'll come back to why that matters particularly for the proposed molten salt thorium reactors). So your comments about the chain reaction are spot on.
And the heat production is a matter of relative levels. To give an example, reactor 1 at Fukushima Dai-ichi would be producing about 1500MW of heat at full power - of which, about 95 MW would be from daughter product decay, so about 6 1/2 % of the total.
As to meltdown risk. No, not really, the confidence is still well placed. TIming is everything. There's a standardised formula for the rate of decay heat production in a light water reaction, and having run it for R1 at Fukushima, the broad picture is 95MW 1 second after shutdown, about 12 MW after an hour, 7 MW after 2 days, and probably now down to about 3-4MW. So, Basically, if you can hold things togeher for the first hour or two, you're into levels where it'd be hard to imagine that the heat generation from melted fuel wouldn't be of an order where it could be lost through the RPV, or to whatever coolant was still coming in.
Basically, the "s** or bust" moment would be if criticality was maintained, so that the fuel was hitting the RPV bottom within seconds or minutes of being in full power output. Even then, I doubt it'd penetrate. You'd have to do a full heat balance of the rate of production, plus the relative heat capacities of the fuel and RPV, plus the rate of loss to remaining coolant and through the RPV wall. TMI was probably as close as you're going to get to that (although there was still lots of water in the vessel), and penetration into the RPV floor was minimal.
Back to "poisons". The reason they feature so prominently in discussions of LFTR designs isn't heat production per se - it's their impact on breeding ratios. Every neutron lost to a poison is one that's not available for breeding fuel.
Before I go any further, I'll declare my hand. I think LFTR desings are well worth exploring. But equally, I think that some of the protagonists either don't understand, or are glossing over some pretty big challenges. I don't see them being "breeders" per se, in the sense of making a surplus of fuel for new reactors to start up, but I think they'll go pretty close to being self-fuelling.
To run an LFTR on a "closed cycle" - i.e making as much fuel as it connsumes - depends utterly on good neutron economy. You have to get fission products out of the salt quickly. for some, that's easy. for example, xenon can be got out of solution simply by spraying (!) the fuel at some stage through an inert atmosphere. Other stuff is harder - and would mean that you had a big inventory of stuff like Iodine on site, outside the relative safety of the main circuit. In some ways, the biggest challenge is something that's part of the actual thorium-uranium cycle, i.e. protactinium. When thorium 232 captures a neutron, it becomes protactinium 233, which then decays back to uranium 233, with a half-life of a month or so. Unfortunately, protactinium 233 rather like to absorm neutrons, so that has to be removed (so it can be taken away and allowed to decay to useful uranium), and that involves delights like bubbling the fuel through a column of liquid bismuth. you also have to do things like sparge flourine through the fuel to extract any uranium made.
So, although from some aspects they look good, they have one f**k of a big chemical process plant stuck on the side, some of it dealing with rather nasty materials like flourine. I suspect that'll be a bigger safety challenge than the reactor itself!
And I'm not entirely convinced about the proposed cooling/safety arrangements. They may not have quite the daughter product burden of conventional reactors, but even if fuel is drained and dumped into cooling tanks, there's still an awful lot of heat to get away - more than the simple air-cooling arrangements talked about would be suitable for.