Wether you are a peasant, middle class or the rich, you have no reason why you shouldn't invest in Bitcoin if you have a source of income, because all you just need is to be financially smart, by knowing how to manage your money very well once your paycheck comes in that's all, because knowing how to arrange your budget is what going to determine how far you can go in your accumulation, because it's through that your source of income you invest and even build your emergency funds, so that you wouldn't have to temper with your holdings if a serious financial emergency situation arise in the future.
Their are some set's of people that would complain that their income is not huge enough to invest in Bitcoin, but they still go out to drink and even gamble, that why I am certain that once an individual have the will to invest, he will always do it if he has a source of income, no excuse, but anyone that doesn't want to do it, will always have a reason why it's not the best time to invest.
You are absolutely right, there is no financial status that cant fit in Bitcoin investment what really counts is an individual being able to plan with the available funds no matter how small it is, many persons started Bitcoin acumulation with as low as $5 or even lower so I believe no excuse or nothing that could hinder an individual from investing in the first place as far as such person has the basic knowledge on how to invest, nothing should limit anyone from investing in Bitcoin, I see anyone giving excuses why he or she can not invest as an unserious person, the reason for DCA method is for every interest person to invest in Bitcoin and what matters is consistency, you start with the amount you want to start with steadily and keep doing the need and may be top up when your income upgrades.
For me I have said that it is not necessary that we will have emergency funds from the beginning, to can build it while we start the investment to avoid it been seen as a tool of procrastination, yea emergency fund is important for every intending and existing investor because this fund helps us not to consider our Bitcoin portfolio as an alternative to solve our immediate problems beside emergency funds have multipurpose, we can use it to buy during the dip if we want and still make use of it to solve immediate or problems as we continue our Bitcoin journey.
Anyone that gives silly complains or excuses that their source is not enough to invest in Bitcoin just as you said, then such person is not really serious about investing in Bitcoin and should not be taken serious too.