In fact if we imagine such a scenario, where someone has all of their fixed income allocation in a mortgage and hundred percent of the portfolio dedicated to Stocks there would be absolutely no difference in behavior following the crash relative to before.(The person would simply keep on making contributions to 100% stocks, or maybe stop making extra payments and contribute a little bit more each month from the mortgage prepayment side to the equities.)
This has nowhere near as dramatic an effect as drawing down liquid bonds and purchasing cheap stocks en masse.
Let's assume somebody has $3000/month to invest, and in "normal" circumstances they're putting $1500/month into equities and $1500/month into mortgage prepayment (above and beyond the minimum). Let's also assume they have a $100,000 house and owe $80,000 (at 4%), and have $20,000 in equities. If the market crashed 50% (and the housing market didn't), then they'd need to "rebalance" $5000 from the mortgage to equities. If they did that by reallocating the $1500/month mortgage prepayment, it would only take them a little over 3 months to rebalance, which (IMO) isn't bad.
In contrast, they could have put the money in BND and be able to rebalance the $5000 immediately,
but at the cost of making 2.5% yield instead of saving 4% in interest. Maybe they come out ahead (if the market rebounds within 3 months,
and they actually executed the rebalance within that window rather than waiting for a "normal" annual rebalance or whatever) in the unusual 50% drop scenario, but they're losing 1.5% the rest of the time.
I admit, this is an extreme example, both because it's a very small portfolio and because it's a very large market correction. A "normal" portfolio would be larger than that and therefore take longer to rebalance... but a "normal" correction would be smaller and therefore require less rebalancing in the first place. I assert (without proof) that the factors more or less cancel each other out.
Now if the person is truly okay with losing 50% of their investment portfolio, then perhaps 100% stock allocation was wise in the first place. But for a person who wants to smooth out the ride and decrease risk, prepaying the mortgage, is simply not an equivalent substitution to a portfolio with bonds in it.
You can't consider the "investment portfolio" in a vacuum; instead you should consider total net worth. If person A has $100,000 in stocks, $0 in bonds, and $50,000 in home equity and the value of their stock drops to $50,000, then they're no worse off than person B who had $100,000 in stocks, $50,000 in bonds, and $0 in home equity. Person B lost 1/3 of his net worth just like person A did.
Now, if you actually need to
use the money (i.e., you're not in the accumulation phase) that's different... but that's not what we we're talking about either.