It always comes down to the math. So, I'm sorry, but that makes this long.
Canadian situation: RRSP's are done with before-tax dollars, money (and whatever it made) is taxed as income when withdrawn.
TFSA (Tax Free Savings Account) - done with after-tax dollars, money (and whatever it made) is withdrawn tax free.
Both have maximums, RRSP is income based, TFSA is flat rate but must be "of age", both can have withdrawals repaid (but there are rules about that).
Mortgage interest is not tax-deductible, there is no capital gain (or loss) on sale of primary residence.
There is capital gains tax when investments are sold, there is income tax on dividend and interest income.
So from a tax viewpoint it does not make sense to save for a mortgage in an account that is not a TFSA, since there will be a big tax hit when the account is cashed.
So again re taxes, where is the person relative to brackets? If at the low end of a bracket, there is lots of room to increase income without penalty - invest. If close to the top of a tax bracket, more investment income will be taxed at the next bracket (not a big deal if the next bracket is not a lot more, but if there is a big jump - ouch - so watch Provincial as well as Federal brackets) - so pay down debt with that money instead. Income has not changed but debt payment is less, so more money is available. Of course this assumes the debt is not overwhelming, in which case it should always be paid down first.
If passive income is high enough (investments, pensions, whatever) then disasters are not disasters. Disaster to your house? Your house insurance should be replacement cost (not original cost, labour and materials have gone up), so you don't find yourself paying costs your insurance company should have. And will your insurance company let you take the money instead? You might not want to rebuild - there may be very negative emotions involved with the disaster. This does not mean you can't have high deductible for less than disastrous situations, to keep premiums reasonable.
Just my $.05 worth (no pennies any more).