I don't have a 7900, but I have a 3800 which is now six years old and going strong.
Just a couple of weeks ago I had my first ever serious nozzle clog, which didn't clear up with a couple of cleanings.
The "Information" tab on the Epson Status Monitor told me that four of my cartridges were manufactured in 2011. This included the two that would clean properly.
I took the old carts out and shook them a few times and tried another nozzle check. No change. Then I replaced all four of the elderly carts and tried again. Now everything is printing just fine again.
This is the first time in six years that I have had any problem with old carts, and yes, the old ones were colors that I seem to use very little of, but I have never had problems with carts only one or two years old.
I expect that the same is true of the 7900, so I would give the old carts a reasonable shake and try them in the new printer, but also invest in some spares for those ones in case you have problems.