I've experienced this same issue with two different Epson WF model printers - in one case the printer was not used frequently enough and in the other case, two of the 4 the ink cartridges were used till they were completely empty but the printer still allowed pages to be printed (the empty colors started showing more streaks and at this point I assumed air was contaminating the lines). This happened with genuine Epson ink for a WF-C5710 MFP. Here is what I did to get the printer working again - not guaranteed to work but it's what I did.
After realizing the ink was completely empty I changed those cartridges and any other cartridges that the printer showed was low (I used generic, 3rd party OEM ink as I knew I'd have to go through many cleaning cycles), then I printed the first nozzle check print out from the printer's on-screen menus. That print showed 2 colours printing properly (magenta, yellow), 2 colours with gaps in the pattern (the ones that were previously completely empty black and cyan) and the printer offered the option of a print head cleaning, which I accepted. After the cleaning I reprinted the nozzle check and was surprised to find that the pattern had degraded severely - the 2 colour printing properly were the same (magenta, mellow) but the 2 other colours had nothing in the pattern (black, cyan), I repeated the cleaning/ nozzle check cycle with the same terrible results (no cyan or black printed in the nozzle check pattern). I did 7 more cleaning followed by nozzle check cycles with no improvement at all. I turned the printer off (using the hardware buttons) and left it overnight to resume the following cycle the next day: nozzle check, followed by 20 printed pages of a CMYK test pattern (found a sample online that had a page of cyan, magenta, yellow, black patterns and blocks), followed by cleaning, followed by a 30 minute pause with no printing. I repeated this throughout the day, sometimes leaving the pauses for longer than 30 minutes depending on my other daily tasks. The results of the nozzle check printed pattern and the CMYK test pattern for the first 9 cycles (on second day) were atrocious with gaps everywhere, completely missing colours (cyan, black), and variation each time was very discouraging (sections that printed fine in a previous cycle would suddenly show many gaps or not print at all). I believe these varying, inconsistent results were the result of air bubbles working their way through the lines - then by the 10th cycle, I was surprised to see the black ink began showing consistently in about 25% of the pattern, but still no cyan. In each subsequent cycle, the black coverage improved and by the 15th cycle I started seeing speckles of cyan, while the black had returned to about 50% coverage (magenta and yellow were always fine). By the 20th cycle, the black was back to 95% and the cyan was 50% coverage (I'm estimating the coverage based on how much the nozzle check pattern was printed for the respective colors). This was a significant improvement from the start of the day. I had to leave the printer overnight and repeat the same thing the next day and eventually got both black and cyan back to 95% coverage of the test pattern - I stopped after that point as I had done over 30 of these cycles, I didn't have the energy to get a 100% perfect nozzle check and the output was sufficient for home use at that point in the recovery.
I think what helped was the printing of the CMYK test pattern pages (to 'exercise' the ink lines by printing enough pages to encourage flow of ink for all the colors and to allow the bubbles to work their way out of the lines) and the pauses to allow the cleaning cycle to "stabilize". It took a lot of cleaning cycles, paper, ink, waiting and patience because the improvement is not steady (and downright discouraging) in the earlier part of the routine. It may not always be worth this effort but I had extra ink (for all the colours) that would have been discarded anyways and I had time.
Going forward I will do what others here have suggested - changing the cartridges soon after the low ink warnings.