Yes, there are many people whose income is not stable, and sometimes they have to face problems when investing. A part of the income can be invested consistently. Especially if you start with a small amount of money, it is not bad. You should start with a small amount of money first and later, if you invest with a discretionary income for long-term investment, the investor can build a large Bitcoin portfolio.
Am thinking otherwise here, because you don't necessarily need to be stable financially for you to invest in Bitcoin and be successful, all that is needed for you to be able to invest in Bitcoin and be successful while holding for a longer run is to have a good money management skills, because even though someone is receiving a salary either weekly or monthly, if he can't manage his finance very well, he will not even have a discretionary funds left to invest with.
Because I have seen those guys that are contractors that doesn't have a stable income, but they still manage to invest with the discretionary income they were able to figure out from the contract they won, so it's more of good money management skills than being stable or not.
I thought the same way as you did and it led me to more innovative ideas but it ended up being a discretionary fund. If you have discretionary funds at the end of the week, you can accumulate Bitcoin with proper management. That means having the right knowledge about Bitcoin no matter the amount is more meaningful. Despite owning a lot of wealth, some people miss out on easy investment opportunities due to lack of proper knowledge about Bitcoin.
Having a stable source of income is not mandatory for Bitcoin If you have a little knowledge about Bitcoin then the ways to accumulate will gradually become understandable. Among them focusing on increasing your source of income and focusing on aggressive accumulating strategies and building an emergency fund through discretionary income. In my opinion as you learn more about Bitcoin you will be able to develop more innovative methods for aggressive accumulation strategies and long term holding.