I've just had an issue with out of date cartridges. I was very dubious as I always think the manufacturers are trying to force you to buy something you don't really need.......
But I was having a problem with the colours on my printer (Epson R800) being very dodgy, particularly when printing high quality photos. Having exhausted just about everything else, in desperation I replaced the cartridges that were out of date, as it suggested doing that in the troubleshooting tips - although some get used up quite quickly, others hardly ever need replacing. They were out of date by about a year.
And hey presto, colours are now perfect. So in my case the use by date did seem to be significant.