What happens if I don't tin my DIY self-etched PCB traces?
The copper corrodes and becomes difficult to solder. If you have not populated the boards, you can simply clean it with a product such as Brasso (image from Amazon):

.. and it will be perfectly solderable once more.
If you assemble the boards and there are a few spots where you need to attach terminals or whatever it will be more difficult because you'll have to selectively clean it. A fiberglass brush-tipped pen may help.
The corrosion is self-limiting in reasonable circumstances and will not affect the board in normal operation in a normal environment, so tinning is unnecessary.
It's possible to coat the board after polishing with a thin layer of organic lacquer-like compound which will protect it for some time. It's called Organic Solderability Preservative (OSP). It's essentially dilute rosin flux with some antifungal agents for humid countries.
P.S. Many years ago I made some etched board prototypes (using a silk screen printing process and etchant, as is done commercially today for mass-produced single-sided boards), and literally tinned them with an electroless Sn plating solution (rather expensive). They looked fine, but when they corroded over a month or so they were actually worse to solder than corroded bare copper.