I totally agree with you, there are folks that has stable source of income but getting a reserve funds is difficult talk more of discretionary, some folks are so useless and careless and yes your kind or type of income doesn't stop you or anyone from Investing as far as they get a discretionary from that source of income and also emergency funds because this fund is very vital when it comes to investing and holding for long. The only disadvantage of having an unstable source of income is that one won't be able to invest intermittently because sometimes this funds can waste time before it comes but a wise investor will device a means to make everything work perfect with the unstable income, it is all about the mind and target.
Its not a compulsory immediately you start having a stable source of income you should start reserving funds and having a discretionary income. You should know that some folks just started having a stable source of income, he has a lot to fix up. For instance, he dont have an apartment, no home appliances and other things that could make him more productive. He has to fix those things first before thinking about starting an investment. There need to be some freedom and flexibility when you start your investment. Its not something you rush into just because you have a stable source of income.