Please provide for me the computations (and your assumptions for those computations), since for any population with a reasonable birthrate (for example, more than 2.1) I can't see it happening at any high rate at all, let alone happening 100% of the time. Clearly, you have some additional factor that I have missed that allows you to support the "probability one" assertion, but you haven't provided what that factor could be.
There are known cases of (even large) families dying out.
That is anecdotal; there are also known cases of small families not dying out, thus once again suggesting that the "probability one" idea is a mistaken one. I'm not discounting that you might indeed be correct, but I simply can't see how your assertion can be even theoretically barely possible, let alone a statistical certainty.
Of course, each new ancestor starts a new tree.
I'm not sure what you mean by this. In the case of mitochondrial DNA, everyone is getting a copy from their mother; the only dieouts happen when the mother has no daughters. Of course, there are going to be mothers who only have sons, but statistically there are more females than males born to humans, so such cases are going to be very short undetectable "twigs" (one or two generations with a mitochondrial dead-end that probably doesn't have any significant genetic drift in any case) in any branching tree, whose destruction is irrelevant to the line (which would be preserved by the daughters of sisters or female cousins, etc.)
A better indication for bottlenecks would be the variance (or variation or other measure of spread) of various genes
Unless you do a full genetic mapping and comparison of the members of a very large sample, that approach doesn't seem to be "a better indicator" at all. Instead, by choosing "various genes" it would seem that you might easily derive terribly inaccurate estimates, something that wouldn't be the case with mitochondrial sampling.
Several such narrow spreads could be used to date such an event. (The Toba hypothesis comes to mind here.)
Exactly. I think the Toba hypothesis is wrong for just this reason (ignoring the other issues, the environmental effects of the eruption are probably overstated and anything that might have caused a bottleneck for the reasonably adaptable and mobile humans should have caused an even more significant decline in various animal species, which should be (but is not) indicated in their genome (a variation of the same problem with the animals for those that believe in the "global" version of the flood myth, except far more specific and damning of the hypothesis in this case).