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That is a fair question and a fair observation. Whilst risking sanctions from others in answering , the solution is credit cards. I did have a bad patch a year or so back involving 3ks worth of vets bills which needed to be covered. I paid most of the bills on the credit cards and waited until the insurance money came in .
I also expect, for various reasons, that I will be out of a job within ten years or so, so there is a medium term element of urgency to pay off the house.
This is a very risk averse strategy though and you could have instead invested that cash tax free through an ISA. Last 5 years annualised global equity return is around 10%. If all your cash is locked up in the property and you have little savings, what happens if you have a large emergency expense?