You can still end up overinvesting and getting your self into the same kind of lack of an emergency fund, even with DCA.
DCA does not completely reduce the problem of overinvesting, but surely it can manage the overinvestment temptations that cause people (maybe moreso newbies, but it can happen to anyone who is overly investing and not sufficiently preparing emergency funds and projecting out cashflows for a sufficient amount of time in advance)..
I get the point now, even with the use of DCA strategy without the plan for emergency funds investment could go very bad were as you could be lack of funds when emergency needs will arise and as such you will be left with no option but to sell from your investment, perhaps I overemphasize DCA on one direction which is to solve the problem of overinvesting and risk management for accumulating a bit by bit forgetting the need for emergency funds which is very important and essential which will help and spice up DCA strategy knowing fully well that as your accumulating using DCA method your also adjusting to your emergency funds.
In this scenario, it depends on whether overinvesting means you've used your emergency fund or this month's rent for your investments. If you require these funds for your bills, it's advisable to withdraw them. Tightening up and assuming you'll be fine even if you lose these funds is not recommended. In my opinion, dollar-cost averaging requires less effort, and it spreads out the risks, effectively removing the emotional aspect, including the risk of overinvesting.
What could lead someone to overinvest when practicing dollar-cost averaging? If a person is using their emergency fund, they are no longer employing dollar-cost averaging, instead, it becomes a direct investment whenever they have cash available. Dollar-cost averaging is explicitly periodic, with investments made at set time intervals, not whenever funds are available. It can be seen as a form of market timing because you're holding back money from investing in order to invest it at a different time.
One of the advantages I find in dollar-cost averaging is that the amount you're investing typically isn't significant enough to cause anxiety about your investments. Constantly adding a small amount can be easily overlooked as you consistently follow this approach.