In my opinion the short answer is NO, but it depends on how important the prints are and how expensive the printer is. Unfortunately most alternative brands aren’t very good. They’re OK for day to day text documents, or even for quick photo prints - say for a meeting - many cheap inks will provide perfectly acceptable results - but for long term use, or if you use a more expensive photo printer - my advice is stick with the original ink. Nobody’s paying me to say this and if I thought cheap inks were just as good, I’d be using them and it would save me a fortune. I have tried independent inks from Jettec in my Canon S9000 and the results were very good but I had to run a cleaning cycle every time I changed an ink cartridge, so I went back to Canon. I’ve used Jettec, Inkrite, Ko-Rec and Print Rite in Epson printers with varying degrees of success - so I have tried this route. The Print-Rite cartridges worked best with the Epson 1290 and the Jettec cartridges seemed OK with my Epson R1800 but the gloss optimizer head blocked up and took a dozen cleaning cycles to clear it. Although most independent ink manufacturers say their ink cartridges are “made to the manufacturers specification” almost all those I’ve tried have led to one problem or another, and that’s before you even consider the biggest problem, which is fading.
In the first fade test I made, the Ko-Rec ink I used looked just as good as the print with Epson’s own ink, when it emerged from the printer, but it faded very badly - Fade Tests - 2000 I’m a professional photographer so I have to make prints that last, so my choice is easy, but if your prints are for the family album, it’s your choice. Just be aware of the downside.
Incidentally I do not include brands like Lyson and Permajet in this. These are specialist inks which unless you buy in bulk, can be just as expensive as the OEM cartridges.
Note: These opinions are based on my own experiences - I’m not affiliated to any printer or ink manufacturer. I buy all my own ink, paper and printers.