Don't you store stmts for 7 years?
I see no reason for a new account.
Why would you want to close your older Chase account? Even though statements older than 7 years are not available you will still have access to statements newer than that. And opening a new Chase account will not give you any access to those older statements. So what would be the benefit of closing the older Chase account and opening a new one?
IMO, I would not close the older Chase account and open a new one. I just don't see any benefit for doing that. Nor do I see any risk for simply keeping your current Chase account open and not opening a new one. I have a Chase credit card that has been open for over 30 yrs and it works just fine. I can't access my credit card statements anywhere near that far back but why would I need to? Once a bank statement has been reconciled there really is no longer any need for it.
BTW, most financial institutions limit the number of years that statements are available for. So, Chase is not alone in this.
You could store the old statements locally, and therefore you would have statements for the full history of the account. I would also rely on good backups. Even though if something goes wrong it will probably be the online account, there isn't 100% guarantee that Quicken won't mess up an offline account.
From my perspective, the 3 most common issues that can occur when deactivating/reactivating an account are:
Generally, troubleshooting for these 3 issues and correcting any issues found will resolve the account balance issue.
These things do not usually happen but they do sometimes happen. I personally would prefer to find the issues and correct for them so I can keep the account continuity in Quicken.
But if you prefer not to spend the time troubleshooting your current account in Quicken you could close your current account in Quicken and then open a new account in Quicken. You do not need to close your current account and open a new one at Chase. Just connect the new account in Quicken with your current account at Chase.
Which path you take is a personal choice.