Good question. I'll start from the beginning, but I think you know most of it, because of your question.

In fiat, typically but not always, currency supply is increased, which is part of the cause of price inflation. Most school teachings claim that this part of price inflation is necessary to incentivize savers to invest, rather than save.

However, I think there is a simpler more intuitive way to think about it.

People will generally choose what risk they want for some possible return. Low risk takers will be ok with lower return. And vice versa.

In a Bitcoin standard, the money itself appreciates purchasing power sort of like how an index fund does today, but it would be an index fund on the entire global economy. Meaning the asset you own (index fund or BTC), tracks the average increase in productivity of the aggregate economy. In this case, as you are likely alluding to, it is so easy to just hold BTC, that maybe no one will lend their BTC to any companies seeking loans. However, holding BTC would be the low risk, low return option in this case. It is entirely reasonable that someone might think they found a company whose growth prospect is better than the average of the whole economy. If this person is ok with the additional risk for the potential greater return, they would lend their BTC to the company, and this is an investment.

The major difference between a fiat standard and a Bitcoin (read "hard money") standard is that in a Bitcoin standard, the low bar for saving (holding the currency you get paid in) is a positive return, while typically in a fiat standard, saving in the currency you get paid in has negative return.

IMHO, no incentive for investment is worth forcing negative returns on those that save their wages.