I would take it all and consolidate to a single system so that there is one single source of truth. Do not throw things out, just prioritize them down where appropriate. But if you throw them out, you land in a CS problem where you get dinged on reviews because "I asked them for this months ago, multiple times. My request was ignored and they say they have no record of even having heard me." Of course, you are not going to do every little one-off request that comes in, but if you don't keep track, you don't know if it is really a one-off request vs. the 8th time some little thing has been asked for in the last 6 months.
Your customers do not care about "start-up time". They want a sustainable, stable product where their feedback has value. Don't throw out that feedback.
I tend to agree with the article, every startup I've worked at has had a large backlog of tickets in JIRA that were completely irrelevant to the current product. That stuff could be pruned pretty easily but never is.
OTOH some of my practices at a very small team would probably be incredibly harmful in a big team, I wouldn't take his advice without considering how it's applicable.
Pass your emails thru that file before hitting SEND and... instant success!
s/todo list/backlog/ s/prototype/mvp/ s/delay/priority adjustment/ ...