It would, but there are limits on how many seeds I can germinate per year and how much storage space I've got (one small airtight box).

I generally only sow about a quarter to half of the seeds I harvest as it is; the rest are just held in reserve for a couple of years in case of catastrophic failure, then cycled out.

I should probably try to remember to add a few extra seeds from some extra random fruit to each year's 'towel', but that requires me to remember which of all the plants I harvested the previous saved seed from! (I do try to take my two seed tomatoes from different plants...)