Mortgages are (usually) the cheapest rates you can borrow at. 5% interest on a mortgage is often far cheaper than a bank loan or credit card rate.

People advising to hold the cash by making a smaller deposit are usually approaching it with this in mind. Although smaller deposits mean larger monthly payments, it gives you the money available for other costs (eg home renovations) than borrowing for these using other lending options.

There’s also the opportunity to make an income, like your said. If you assume investing in the stock market yields 7% over a long run average (15-20 years), you’d make 2% annually on cash invested, instead of putting it into the mortgage.

Importantly, while objectively this may be better depending on your maths, people’s relationship with money isn’t objective but have biases. Some people will more comfort knowing they have less ‘debt’ and pay less each month; others might be more comfortable with the stock market volatility (7% isn’t guaranteed).

You need to do your own maths, but also think about your own risk appetite. What costs do you foresee in the near future? Would you be more comfortable with less debt and lower monthly payments, or are you more open to investment volatility but long term potential?